@Book{AdLo94, author = {W.~Adams and P.~Loustaunau}, title = {An Introduction to Gr\"obner Bases}, publisher = {Graduate Studies in Mathematics, AMS, Providence}, year = {1994} } @Unpublished{Al95, author = {M.~E.~Alonso et al.}, title = {The Big Mother of All the Dualities}, note = {Draft}, year = 1995 } @PhdThesis{Ap88, author = {J.~Apel}, title = {{Gr\"obnerbasen} in {nichtkommutativen} {Algebren} und ihre {Anwendung}}, school = {Universit\"at Leipzig}, year = 1988 } @Article{Ap95, author = {J.~Apel}, title = {A {G}r\"obner Approach to Involutive Bases}, journal = {Journal of Symbolic Computation}, year = 1995, volume = 19, number = 5, pages = {441-457} } @PhdThesis{Ap98, author = {J.~Apel}, title = {Zu Berechenbarkeitsfragen der Idealtheorie}, school = {Universit\"at Leipzig}, year = 1998, type = {Habilitationsschrift} } @Article{ApLa88, author = {J.~Apel and W.~Lassner}, title = {An Extension of {Buchberger's} Algorithm and Calculations in Enveloping Fields of {L}ie Algebras}, journal = {Journal of Symbolic Computation}, year = 1988, volume = 6, pages = {361-370} } @Article{AvMa84, author = {J.~Avenhaus and K.~Madlener}, title = {The {Nielsen} Reduction and P-Complete Problems in Free Groups}, journal = {Theoretical Computer Science}, year = 1984, volume = 32, pages = {61-76} } @Article{AvMaOt86, author = {J.~Avenhaus and K.~Madlener and F.~Otto}, title = {Groups Presented by Finite Two-Monadic {C}hurch-{R}osser Thue Systems}, journal = {Transactions of the American Mathematical Society}, year = 1986, volume = 297, pages = {427-443} } @InProceedings{AvWi89, author = {J.~Avenhaus and D.~Wi{\ss}mann}, title = {Using Rewriting Techniques to Solve the Generalized Word Problem in Polycyclic Groups}, booktitle = {Proc.~ISSAC'89}, year = 1989, pages = {322-337}, editor = {G.~Gonnet}, publisher = {ACM} } @Unpublished{BBM98, author = {M.~A.~Borges and M.~Borges and T.~Mora}, title = {Non-commutative Gr\"obner Bases and FGLM Techniques}, note = {Draft}, year = 1998 } @PhdThesis{Ba81, author = {G.~Bauer}, title = {Zur {Darstellung} von {Monoiden} durch {konfluente} {Reduktionssysteme}}, school = {Universit\"at Kaiserslautern}, year = 1981 } @InProceedings{Ba89, author = {F.~Baader}, title = {Unification in Commutative Theories, Hilbert's Basis Theorem and Gr\"obner Bases}, booktitle = {Proc.~UNIF'89}, year = 1989 } @Article{BaCaMi81, author = {G.~Baumslag and D.~Cannonito and C.~Miller}, title = {Computable Algebra and Group Embeddings}, journal = {Journal of Algebra}, year = 1981, volume = 69, pages = {186-212} } @Article{BaGa94a, author = {L.~Bachmair and H.~Ganzinger}, title = {Rewrite-Based Equational Theorem Proving With Selection Simplification}, journal = {Journal of Symbolic Computation}, year = 1994, volume = 4, number = 3, pages = {1-31} } @InProceedings{BaGa94b, author = {L.~Bachmair and H.~Ganzinger}, title = {Buchberger's algorithm: A constraint-based completion procedure}, booktitle = {Proc.~CCL'94}, year = 1994, pages = {285-301} } @Book{BeKeRi87, author = {B.~Benninghofen and S.~Kemmerich and M.M.~Richter}, title = {Systems of Reductions}, publisher = {Springer}, year = 1987, series = {LNCS 277} } @InProceedings{BeSe97, author = {J.~Bently and R.~Sedgewick}, title = {Fast Algorithms for Sorting and Searching Strings}, booktitle = {8th Annual ACM-SIAM Symposium on Discrete Algorithms}, year = 1997 } @Book{BeWe92, author = {T.~Becker and V.~Weispfenning}, title = {Gr\"obner Bases - A Computational Approach to Commutative Algebra}, publisher = {Springer}, year = 1992 } @InProceedings{BoBo98, author = {M.~A.~Borges and M.~Borges}, title = {Gr\"obner Bases Property on Elimination Ideal in the Noncommutative Case}, booktitle = {Gr\"obner Bases and Applications (Proc. of the Conference 33 Years of Gr\"obner Bases)}, editor = {B.~Buchberger and F.~Winkler}, series = {London Mathematical Society Lecture Notes Series}, volume = 251, year = 1998, publisher = {Cambridge University Press}, pages = {323--337} } @Book{BoOt93, author = {R.~Book and F.~Otto}, title = {String Rewriting Systems}, publisher = {Springer}, year = 1993 } @PhdThesis{Bu65, author = {B.~Buchberger}, title = {Ein {Algorithmu}s zum {Auffinden} der {Basiselemente} des {Restklassenrings} nach einem {nulldimensionalen} {Polynomideal}}, school = {Universit\"at Innsbruck}, year = 1965 } @Article{Bu70, author = {B.~Buchberger}, title = {Ein algorithmisches Kriterium f\"ur die L\"osbarkeit eines algebraischen Gleichungssystems}, journal = {Aequ. Math. 4/3}, year = {1970}, OPTpages = {374-383} } @InProceedings{Bu83, author = {B.~Buchberger}, title = {A Critical-Pair Completion Algorithm for Finitely Generated Ideals in Rings}, booktitle = {Proc.~Logic and Machines: Decision Problems and Complexity}, publisher = {Springer}, series = {LNCS 171}, year = 1983, pages = {137-161} } @InCollection{Bu85, author = {B.~Buchberger}, title = {Gr\"obner Bases: An Algorithmic Method in Polynomial Ideal Theory}, booktitle = {Multidimensional Systems Theory}, publisher = {Reidel, Dordrecht}, year = 1985, editor = {N.~K.~Bose}, chapter = 6, pages = {184-232} } @InCollection{Bu87, author = {B.~Buchberger}, title = {Applications of {G}r\"obner Bases in Non-Linear Computational Geometry}, booktitle = {Trends in Computer Algebra}, publisher = {Springer}, year = 1987, editor = {R.~Jan{\ss}en}, series = {LNCS 296}, pages = {52-80} } @InProceedings{BuMo81, author = {B.~Buchberger and M.~M\"oller}, title = {The Construction of Multivariate Polynomials with Preassigned Zeroes}, booktitle = {EUROCAM}, publisher = {Springer}, series = {LNCS 144}, year = 1982, pages = {24-31} } @Book{CoLiOS92, author = {D.~Cox and J.~Little and D.~O'Shea}, title = {Ideals, Varieties, and Algorithms}, publisher = {Springer}, year = 1992 } @PhdThesis{Cr95, author = {R.~Cremanns}, title = {Finiteness Conditions for Rewriting Systems}, school = {Universit\"at Gesamthochschule Kassel}, year = 1995 } @InProceedings{CrOt94, author = {R.~Cremanns and F.~Otto}, title = {Constructing Canonical Presentations for Subgroups of Context-Free Groups in Polynomial Time}, booktitle = {Proc.~ISSAC'94}, year = 1994, pages = {147-153}, editor = {J.~von zur Gathen and M.~Giesbrecht}, publisher = {ACM} } @Article{De12, author = {M.~Dehn}, title = {\"Uber {unendliche} {diskontinuierliche} {Gruppen}}, journal = {Mathematische Annalen}, year = 1912, volume = 71, pages = {116-144} } @MastersThesis{De89, author = {T.~Dei{\ss}}, title = {{B}e\-rech\-nung von {G}r\"obner\-basen, effizienz\-steigernde {M}a{\ss}\-nahmen und {R}est\-klassen\-ringe als {K}oeffizientenbereich}, school = {Universit\"at Kaiserslautern}, year = 1989 } @InProceedings{De92, author = {T.~Dei{\ss}}, title = {Conditional Semi-{T}hue Systems for Presenting Monoids}, booktitle = {Proc.~STACS'92}, year = 1992, pages = {557-565} } @Article{Di86, author = {V.~Diekert}, title = {Commutative Monoids Have Complete Presentations by Free (Non-Commutative) Monoids}, journal = {Theoretical Computer Science}, year = 1986, volume = 46, pages = {319-327} } @TechReport{Es86, author = {C.~Eschenbach}, title = {Die {Verwendung} von {Z}ei\-chen\-ket\-ten\-ord\-nungen im {Z}u\-sam\-men\-hang mit {S}emi-{T}hue {S}ystemen}, institution = {Universit\"at Hamburg}, year = 1986 } @Article{FGLM93, author = {J.~C.~Faug\`ere and P.~Gianni and D.~Lazard and T.~Mora}, title = {Efficient Computation of Zero-dimensional {G}r\"obner Bases by Change of Ordering}, journal = {Journal of Symbolic Computation}, year = 1993, volume = 16, pages = {329-344} } @Article{FaFeGr93, author = {D.~Farkas and C.~Feustel, E.~Green}, title = {Synergy in the Theories of {G}r\"obner Bases and Path Algebras}, journal = {Canadian Journal of Mathematics}, year = 1993, volume = 45, number = 4, pages = {727-739} } @InProceedings{Ga85, author = {A.~Galligo}, title = {Some Algorithmic Questions on Ideals of Differential Operators}, booktitle = {Proc.~EUROCAL'85}, series = {LNCS}, volume = 204, year = 1985, publisher = {Springer}, pages = {413-421} } @Article{GaLa88, author = {T.~Gateva-Ivanova and V.~Latyshev}, title = {On Recognizable Properties of Associative Algebras}, journal = {Journal of Symbolic Computation}, year = 1988, volume = 6, pages = {371-388} } @Book{GeCzLa92, author = {K.~O.~Geddes and S.~R.~Czapor and G.~Labahn}, title = {Algorithms for Computer Algebra}, publisher = {Kluwer Academic Publishers, Massachusettes}, year = 1992 } @Article{Gi79, author = {R.~Gilman}, title = {Presentations of Groups and Monoids}, journal = {Journal of Algebra}, year = 1979, volume = 57, pages = {544-554} } @Book{Ha59, author = {M.~Hall Jr.~}, title = {The Theory of Groups}, publisher = {Chelsea Publishing Company}, year = 1959, address = {New York} } @Article{He26, author = {G.~Hermann}, title = {Die {F}rage der endlich vielen {S}chritte in der {T}heorie der {P}olynomideale}, journal = {Mathematische Annalen}, year = 1926, volume = 95, pages = {737-788} } @Book{He64, author = {I.~N.~Herstein}, title = {Topics in Algebra}, publisher = {Xerox College Publishing}, year = 1964, address = {Lexington, Massachusetts, Toronto} } @Article{Hi64, author = {H.~Hironaka}, title = {Resolution of Singularities of an Algebraic Variety over a Field of Characteristic Zero}, journal = {Annals of Mathematics}, year = 1964, volume = 79, pages = {109-326} } @Article{Hu80, author = {G.~Huet}, title = {Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems}, journal = {Journal of the ACM}, year = 1980, volume = 27, number = 4, pages = {797-821} } @Article{Hu81, author = {G.~Huet}, title = {A Complete Proof of Correctness of the {K}nuth-{B}endix Completion Algorithm}, journal = {Journal of Computer and System Science}, year = 1981, volume = 23, number = 1, pages = {11-21} } @Article{Ja81, author = {M.~Jantzen}, title = {On a Special Monoid with Single Defining Relation}, journal = {Theoretical Computer Science}, year = 1981, volume = 16, pages = {61-73} } @Article{Ja85, author = {M.~Jantzen}, title = {A Note on a Special One-rule Semi-Thue System}, journal = {Information Processing Letters}, year = 1985, volume = 21, pages = {135-140} } @Book{Jo76, author = {D.~L.~Johnson}, title = {Presentation of Groups}, publisher = {Cambridge University Press}, year = 1976 } @TechReport{KaKa84, author = {A.~Kandri-Rody and D.~Kapur}, title = {An Algorithm for Computing the {G}r\"obner Basis of a Polynomial Ideal over an {E}uclidean Ring}, institution = {General Electric Company Corporate Research and Development}, year = 1984, key = {Technical Information Series}, address = {Schenectady, NY 12345}, month = {December} } @Article{KaKa88, author = {A.~Kandri-Rody and D.~Kapur}, title = {Computing a {G}r\"obner Basis of a Polynomial Ideal over an {E}uclidean domain}, journal = {Journal of Symbolic Computation}, year = 1988, volume = 6, pages = {37-57} } @InProceedings{KaKaWi89, author = {A.~Kandri-Rody and D.~Kapur and F.~Winkler}, title = {{K}nuth-{B}endix Procedure and {B}uchberger Algorithm -- a Synthesis}, booktitle = {Proc. ISSAC'89}, year = 1989, pages = {55-67}, editor = {G.~Gonnet}, publisher = {ACM} } @InCollection{KaMa89, author = {D.~Kapur and K.~Madlener}, title = {A Completion Procedure for Computing a Canonical Basis for a k-Subalgebra}, booktitle = {Computers and Mathematics}, publisher = {Springer}, year = 1989, pages = {1-11} } @Book{KaMe79, author = {M.~I.~Kargapolov and Ju.~I.~Merzljakov}, title = {Fundamentals of the Theory of Groups}, publisher = {Springer}, year = 1979 } @Article{KaNa85, author = {D.~Kapur and P.~Narendran}, title = {A Finite Thue System with Decidable Word Problem and Without Equivalent Finite Canonical System}, journal = {Theoretical Computer Science}, year = 1985, volume = 35, pages = {337-344} } @Article{KaWe90, author = {A.~Kandri-Rody and V.~Weispfenning}, title = {Non-Commutative {G}r\"obner Bases in Algebras of Solvable Type}, journal = {Journal of Symbolic Computation}, year = 1990, volume = 9, pages = {1-26} } @InProceedings{Ke97, author = {B.~J.~Keller}, title = {Alternatives in Implementing Noncommutative {G}r\"obner Basis Systems}, booktitle = {Proceedings of the Workshop on Symbolic Rewriting Techniques, Monte Verita, 1995}, year = {1998}, publisher = {Birkh\"auser}, pages = {127-180} } @InCollection{KnBe70, author = {D.~Knuth and P.~Bendix}, title = {Simple Word Problems in Universal Algebras}, booktitle = {Computational Problems in Abstract Algebra}, publisher = {Pergamon Press, Oxford}, year = 1970, editor = {J.~Leech}, pages = {263-297} } @Book{Kr93, author = {H.~Kredel}, title = {Solvable Polynomial Rings}, publisher = {Verlag Shaker}, year = 1993, address = {Aachen} } @PhdThesis{Ku91, author = {N.~Kuhn}, title = {Zur {E}nt\-scheid\-bar\-keit des {U}n\-ter\-grup\-pen\-pro\-blems f\"ur {G}rup\-pen mit ka\-non\-ischen {D}ar\-stel\-lungen}, school = {Universit\"at Kaiserslautern}, year = 1991 } @InProceedings{KuMa89, author = {N.~Kuhn and K.~Madlener}, title = {A Method for Enumerating Cosets of a Group Presented by a Canonical System}, booktitle = {Proc.~ISSAC'89}, year = 1989, pages = {338-350}, editor = {G.~Gonnet}, publisher = {ACM} } @Article{KuMaOt94, author = {N.~Kuhn and K.~Madlener and F.~Otto}, title = {Computing Presentations for Subgroups of Polycyclic Groups and of Context-Free Groups}, journal = {Applicable Algebra in Engineering, Communication and Computing}, year = 1994, volume = 5, pages = {287-316} } @MastersThesis{La76, author = {M.~Lauer}, title = {Ka\-non\-ische {R}e\-pr\"a\-sen\-tan\-ten f\"ur die {R}est\-klas\-sen nach einem {P}oly\-nom\-ideal}, school = {Universit\"at Kaiserslautern}, year = 1976 } @Book{La79, author = {G.~Lallement}, title = {Semigroups and Combinatorial Applications}, publisher = {John Wiley \& Sons, New York}, year = 1979 } @InProceedings{La85, author = {W.~Lassner}, title = {Symbol Representations of Noncommutative Algebras}, booktitle = {EUROCAL'85}, series = {LNCS 204}, year = 1985, publisher = {Springer}, pages = {99-115} } @Article{La90, author = {G.~Labont\'e}, title = {An Algorithm for the Construction of Matrix Representations for Finitely Presented Non-comutative Algebras}, journal = {Journal of Symbolic Computation}, year = 1990, volume = 9, pages = {27-38} } @Book{LeDe91, author = {H.~Lewis and L.~Denenberg}, title = {Data Structures \& Their Algorithms}, publisher = {Harper Collins}, year = 1991 } @Misc{Leda, title = {{\sc Leda}: http://www.mpi-sb.mpg.de/leda/leda.html} } @Article{Li91, author = {S.~Linton}, title = {Constructing Matrix Representations of Finitely Presented Groups}, journal = {Journal of Symbolic Computation}, year = 1991, volume = 12, pages = {427-438} } @PhdThesis{Lo96, author = {E.~Lo}, title = {A Polycyclic Quotient Algorithm}, school = {Rutgers}, year = 1996, address = {New Brunswick, New Jersey} } @Article{Lo98, author = {E.~Lo}, title = {A Polycyclic Quotient Algorithm}, journal = {Journal of Symbolic Computation}, year = 1998, volume = 25, number = 1 } @Book{LySch77, author = {R.~C.~Lyndon and P.~E.~Schupp}, title = {Combinatorial Group Theory}, publisher = {Springer}, year = 1977 } @Unpublished{Ma86, author = {K.~Madlener}, title = {Existence and Construction of {G}r\"obner Bases for Ideals in Reduction Rings}, note = {Universit\"at Kaiserslautern}, year = 1986 } @Book{MaKaSo76, author = {W.~Magnus and A.~Karrass and D.~Solitar}, title = {Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations}, publisher = {Dover Publications, New York}, year = 1976 } @InCollection{MaMeSa93, author = {S.~Margolis and J.~Meakin and M.~Sapir}, title = {Algorithmic Problems in Groups, Semigroups and Inverse Monoids}, booktitle = {Semigroups, Formal Languages and Groups}, publisher = {Kluwer Academic Press}, year = 1993, editor = {J.~Fountain}, pages = {147-214} } @Article{MaMoMo93, author = {M.~G.~Marinari and H.~M.~M\"oller and T.~Mora}, title = {Gr\"obner Bases of Ideals Defined by Functionals with an Application to Ideals of Projective Points}, journal = {Applicable Algebra in Engineering, Communication and Computing}, year = 1993, volume = 4, pages = {103-145} } @TechReport{MaMoRe98a, author = {B.~Reinert and K.~Madlener and T.~Mora}, title = {A Note on Nielsen Reduction and Coset Enumeration}, institution = {Centre of Computer Algebra}, year = 1997, type = {Reports on Computer Algebra}, number = 14, address = {Universit\"at Kaiserslautern} } @Article{MaOt89, author = {K.~Madlener and F.~Otto}, title = {About the Descriptive Power of Certain Classes of Finite String-Rewriting Systems}, journal = {Theoretical Computer Science}, year = 1989, volume = 67, pages = {143-172} } @InCollection{MaOt93, author = {K.~Madlener and F.~Otto}, title = {Some Undecidability Results for Finitely Generated Thue Congruences on a Two-Letter Alphabet}, booktitle = {Beitr\"age zur Angewandten Analysis und Informatik, Helmut Brakhage zu Ehren}, publisher = {Verlag Shaker}, year = 1994, editor = {E.~Schock}, pages = {248-261}, address = {Aachen} } @Article{MaOt97, author = {K.~Madlener and F.~Otto}, title = {Some Undecidability Results for Finitely Generated Thue Congruences on a Two-Letter Alphabet}, journal = {Fundamenta Informatica}, year = 1997, volume = 30, number = 1, pages = {31-44} } @InCollection{MaOt98, author = {Madlener, K. and Otto, F.}, title = {{Some Applications Of Prefix-Rewriting In Monoids, Groups, And Rings}}, year = "1998", month = "November", booktitle = "Reports On Computer Algebra", publisher = "Centre for Computer Algebra, University of Kaiserslautern", number = 22, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @TechReport{MaRe93a, author = {K.~Madlener and B.~Reinert}, title = {On {G}r\"obner Bases in Monoid and Group Rings}, institution = {Universit\"at Kaiserslautern}, year = 1993, type = {SEKI Report}, number = {SR-93-08} } @InProceedings{MaRe93b, author = {K.~Madlener and B.~Reinert}, title = {Computing {G}r\"obner Bases in Monoid and Group Rings}, booktitle = {Proc.~ISSAC'93}, year = 1993, pages = {254-263}, editor = {M.~Bronstein}, publisher = {ACM} } @InProceedings{MaRe95, author = {K.~Madlener and B.~Reinert}, title = {String Rewriting and {G}r\"obner Bases -- A General Approach to Monoid and Group Rings}, booktitle = {Proceedings of the Workshop on Symbolic Rewriting Techniques, Monte Verita, 1995}, year = {1998}, series = {Progress in Computer Science and Applied Logic}, volume = 15, publisher = {Birkh\"auser}, editor = {M.~Bronstein and J.~Grabmeier and V.~Weispfenning}, pages = {127-180} } @TechReport{MaRe96a, author = {K.~Madlener and B.~Reinert}, title = {String Rewriting and {G}r\"obner Bases -- A General Approach to Monoid and Group Rings}, institution = {Centre of Computer Algebra, Universit\"at Kaiserslautern}, year = 1997, type = {Reports on Computer Algebra}, number = 16, address = {Universit\"at Kaiserslautern}, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @Article{MaRe96b, author = {K.~Madlener and B.~Reinert}, title = {A Generalization of {G}r\"obner Bases Algorithms to Nilpotent Group Rings}, journal = {Applicable Algebra in Engineering, Communication and Computing}, year = 1997, volume = 8, number = 2, pages = {103-123} } @Article{MaRe97a, author = {K.~Madlener and B.~Reinert}, title = {A Generalization of {G}r\"obner Basis Algorithms to Polycyclic Group Rings}, journal = {Journal of Symbolic Computation}, year = {1998}, volume = 25, number = 1, pages = {23-45} } @Article{MaRe97c, author = {K.~Madlener and B.~Reinert}, title = {Relating Rewriting Techniques on Monoids and Rings: Congruences on Monoids and Ideals in Monoid Rings}, journal = {Theoretical Computer Science}, year = {1998}, volume = {208}, pages = {3-31} } @TechReport{MaRe97b, author = {K.~Madlener and B.~Reinert}, title = {Relating Rewriting Techniques on Monoids and Rings: Congruences on Monoids and Ideals in Monoid Rings}, institution = {Centre of Computer Algebra}, year = 1997, type = {Reports on Computer Algebra}, number = 14, address = {Universit\"at Kaiserslautern}, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @InProceedings{MaRe98, author = {K.~Madlener and B.~Reinert}, title = {Gr\"obner Bases in Non-Commutative Reduction Rings}, booktitle = {Gr\"obner Bases and Applications (Proc. of the Conference 33 Years of Gr\"obner Bases)}, editor = {B.~Buchberger and F.~Winkler}, series = {London Mathematical Society Lecture Notes Series}, volume = 251, year = 1998, publisher = {Cambridge University Press}, pages = {408-420} } @TechReport{McN97, author = {R.~McNaughton}, title = {The Finiteness of Finitely Presented Monoids}, institution = {Rensselaer Polytechnic Institute}, year = 1997 } @InCollection{Mi91, author = {C.~F.~Miller}, title = {Decision Problems for Groups -- Survey and Reflections}, booktitle = {Algorithms and Classification in Combinatorial Group Theory}, publisher = {Springer}, year = 1991, pages = {1-60} } @Article{Mi96, author = {J.~L.~Miller}, title = {Analogs of {G}r\"obner Bases in Polynomial Rings over a Ring}, journal = {Journal of Symbolic Computation}, year = 1996, volume = 21, pages = {139-153} } @InProceedings{Mo85, author = {F.~Mora}, title = {Gr\"obner Bases for Non-Commutative Polynomial Rings}, booktitle = {Proc.~AAECC-3}, series = {LNCS 229}, year = 1985, publisher = {Springer}, pages = {353-362} } @Unpublished{Mo87, author = {T.~Mora}, title = {Gr\"obner Bases and the Word Problem}, note = {Genova}, year = 1987 } @InProceedings{Mo88, author = {T.~Mora}, title = {Gr\"obner Bases for Non-Commutative Algebras}, booktitle = {Proc.~of ISSAC'88}, series = {LNCS 358}, year = 1989, pages = {150-161} } @Article{Mo94, author = {T.~Mora}, title = {An Introduction to Commutative and Non-Commutative {G}r\"obner Bases}, journal = {Theoretical Computer Science}, year = 1994, volume = 134, pages = {131-173} } @InProceedings{MoMoTr92, author = {H.~M.~M\"oller and T.~Mora and C.~Traverso}, title = {Gr\"obner Bases Computation Using Syzygies}, booktitle = {Proc. ISSAC'92}, year = 1992, pages = {320-328}, editor = {P.~Wang}, publisher = {ACM} } @Article{NaOD89, author = {P.~Narendran and C.~\'{O}'D\'{u}nlaing}, title = {Cancellativity in Finitely Presented Semigroups}, journal = {Journal of Symbolic Computation}, year = 1989, volume = 6, pages = {457-472} } @Article{Ne67, author = {B.~H.~Neumann}, title = {Some Remarks on Semigroup Presentations}, journal = {Canadian Journal of Mathematics}, year = 1967, volume = 19, pages = {1018-1026} } @InCollection{Ne81, author = {J.~Neub\"user}, title = {An Elementary Introduction to Coset Table Methods in Computational Group Theory}, booktitle = {Groups St. Andrews 1981}, publisher = {Cambridge University Press}, year = 1982, editor = {C.~M.~Campbell and E.~F.~Robertson}, series = {L.M.S.~Lecture Notes 71}, pages = {1-45} } @Article{Ni21, author = {J.~Nielsen}, title = {Om {Regning} med ikke {kommutative} {Faktoren} og dens {Anvendelse} i {Gruppeteorien}}, journal = {Mat.~Tidsskr.~B.}, year = 1921, pages = {77-94} } @Article{OD83, author = {C.~\'{O}'D\'{u}nlaing}, title = {Undecidable Questions Related to {C}hurch-{R}osser {T}hue Systems}, journal = {Theoretical Computer Science}, year = 1983, volume = 23, pages = {339-345} } @TechReport{Pa85, author = {L.~Pan}, title = {On the {G}r\"obner Bases of Ideals in Polynomial Rings over a Prinicipal Ideal Domain}, institution = {Department of Mathematics, University of California}, year = 1985, address = {Santa Barbara} } @PhdThesis{Pe97, author = {M.~Pesch}, title = {Gr\"obner Bases in Skew Polynomial Rings}, school = {Universit\"at Passau}, year = 1997 } @InProceedings{Pe98, author = {M.~Pesch}, title = {Two-Sided Gr\"obner Bases in Iterated Ore Extensions}, booktitle = {Proceedings of the Workshop on Symbolic Rewriting Techniques, Monte Verita, 1995}, year = {1998}, series = {Progress in Computer Science and Applied Logic}, volume = 15, publisher = {Birkh\"auser}, editor = {M.~Bronstein and J.~Grabmeier and V.~Weispfenning} } @PhdThesis{Re95, author = {B.~Reinert}, title = {On {G}r\"obner Bases in Monoid and Group Rings}, school = {Universit\"at Kaiserslautern}, year = 1995 } @TechReport{Re96, author = {B.~Reinert}, title = {Introducing Reduction to Polycyclic Group Rings - A Comparison of Methods}, institution = {Centre of Computer Algebra, Universit\"at Kaiserslautern}, year = 1996, type = {Reports on Computer Algebra}, number = {9}, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @InCollection{Re98, author = {B.~Reinert}, title = {Observations on Coset Enumeration}, institution = {Centre of Computer Algebra, Universit\"at Kaiserslautern}, year = 1998, type = {Reports on Computer Algebra}, number = {23}, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @InCollection{Re00a, author = {B.~Reinert}, title = {Solving One-sided Equations in Integer Monoid Rings}, institution = {Centre of Computer Algebra, Universit\"at Kaiserslautern}, year = 2000, type = {Reports on Computer Algebra}, number = {26}, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @TechReport{Re99a, author = {B.~Reinert}, title = {Coset Enumeration -- A Comparison of Methods}, institution = {Centre of Computer Algebra, Universit\"at Kaiserslautern}, year = {to appear} } @TechReport{Re99b, author = {B.~Reinert}, title = {Comparing String Rewriting Methods for Coset Enumeration}, institution = {Centre of Computer Algebra, Universit\"at Kaiserslautern}, year = {to appear} } @InProceedings{ReMoMa98, author = {B.~Reinert and T.~Mora and K.~Madlener}, title = {A Note on Nielsen Reduction and Coset Enumeration}, booktitle = {Proc.~ISSAC'98}, year = 1998, pages = {171-178}, editor = {O.~Gloor}, publisher = {ACM} } @InProceedings{Re00, author = {B.~Reinert}, title = {Solving Systems of Linear One-Sided Equations in Integer Monoid and Group Rings}, booktitle = {Proc.~ISSAC'00}, year = 2000, editor = {C.~Traverso}, pages = {281-287}, publisher = {ACM} } @TechReport{ReZe98, author = {B.~Reinert and D.~Zeckzer}, title = {User Reference for {\sc Mrc}: A System for Computing {G}r\"obner Bases in monoid and Group Rings}, institution = {Universit\"at Kaiserslautern}, year = 1998, type = {Reports on Computer Algebra}, number = {20}, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @InProceedings{ReZe98a, author = {B.~Reinert and D.~Zeckzer}, title = {{\sc Mrc}: A System for Computing {G}r\"obner Bases in Monoid and Group Rings}, booktitle = {6th Rhine Workshop on Computer Algebra, Sankt Augustin}, year = 1998 } @Article{ReZe99, author = {B.~Reinert and D.~Zeckzer}, title = {MRC - Data Structures and Algorithms for Computing in Monoid and Group Rings}, journal = {Applicable Algebra in Engineering, Communications and Computing}, year = 1999, volume = 10, number = 1, pages = {41-78} } @InCollection{ReZe99a, author = {B.~Reinert and D.~Zeckzer}, title = {Coset Enumeration using Prefix Gr\"obner Bases in {\sc Mrc} -- An Experimental Approach}, institution = {Centre of Computer Algebra, Universit\"at Kaiserslautern}, year = 1999, type = {Reports on Computer Algebra}, number = {25}, note = "Online available at http://www.mathematik.uni-kl.de/\textasciitilde zca" } @Article{Ro93, author = {A.~Rosenmann}, title = {An Algorithm for Constructing {G}r\"obner and Free {S}chreier Bases in Free Group Algebras}, journal = {Journal of Symbolic Computation}, year = 1993, volume = 16, pages = {523-549} } @InProceedings{RoSw90, author = {L.~Robbiano and M.~Sweedler}, title = {Subalgebra Bases}, booktitle = {Proc.~Commutative Algebra Salvador}, editor = {W.~Burns and A.~Simis}, series = {LNM 1430}, year = 1990, publisher = {Springer}, pages = {61-87} } @PhdThesis{Sa96, author = {A.~Sattler-Klein}, title = {A Systematic Study of Infinite Canonical Systems generated by Knuth-Bendix Completion and Related Problems}, school = {Universit\"at Kaiserslauter}, year = 1996 } @Article{ShSw88, author = {D.~Shannon and M.~Sweedler}, title = {Using {G}r\"obner Bases to Determine Algebra Membership, Split Surjective Algebra Homomorphisms Determine Birational Equivalence}, journal = {Journal of Symbolic Computation}, year = 1988, volume = 6, pages = {267-273} } @Article{Si90, author = {C.~Sims}, title = {Implementing the {B}aumslag-{C}annonito-{M}iller Polycyclic Quotient Algorithm}, journal = {Journal of Symbolic Computation}, year = 1990, volume = 9, pages = {707-723} } @Article{Si91, author = {C.~Sims}, title = {The {K}nuth-{B}endix Procedure for Strings as a Substitute for Coset Enumertation}, journal = {Journal of Symbolic Computation}, year = 1991, volume = 12, pages = {439-442} } @Book{Si94, author = {C.~Sims}, title = {Computation with Finitely Presented Groups}, publisher = {Cambridge University Press}, year = 1994 } @Article{Sq87, author = {C.~Squier}, title = {Word Problems and a Homological Finiteness Condition for Monoids}, journal = {Journal of Pure Applied Algebra}, year = 1987, volume = 49, pages = {201-217} } @Article{St87, author = {S.~Stifter}, title = { A Generalization of Reduction Rings}, journal = {Journal of Symbolic Computation}, year = 1987, volume = 4, pages = {351-364} } @Article{St90, author = {T.~Stokes}, title = {Gr\"obner Bases in Exterior Algebras}, journal = {Journal of Automated Reasoning}, year = 1990, volume = 6, pages = {233-250} } @InProceedings{ToCo36, author = {J.~Todd and H.~Coxeter}, title = {A Practical Method for Enumerating Cosets of a Finite Abstract Group}, booktitle = {Proc. Edinburgh Math. Soc.}, year = 1936, volume = 5, pages = {26-34} } @Article{Tr78, author = {W.~Trinks}, title = {{\"Uber B.~Buchbergers Verfahren, Systeme algebraischer Gleichungen zu l\"osen}}, journal = {Journal of Number Theory}, year = {1978}, volume = {10(4)}, pages = {475-488}, } @InProceedings{Uf98, author = {V.~Ufnarovski}, title = {Introduction to Noncommutative Gr\"obner Bases Theory}, booktitle = {Gr\"obner Bases and Applications (Proc. of the Conference 33 Years of Gr\"obner Bases)}, editor = {B.~Buchberger and F.~Winkler}, series = {London Mathematical Society Lecture Notes Series}, volume = 251, year = 1998, publisher = {Cambridge University Press}, pages = {259-280} } @InProceedings{We87, author = {V.~Weispfenning}, title = {Gr\"obner Basis for Polynomial Ideals over Commutative Regular Rings}, booktitle = {Proc. EUROCAL'87}, series = {LNCS 378}, year = 1987, publisher = {Springer}, pages = {336-347} } @InProceedings{We92, author = {V.~Weispfenning}, title = {Finite {G}r\"obner Bases in Non-Noetherian Skew Polynomial Rings}, booktitle = {Proc. ISSAC'92}, year = 1987, pages = {329-334}, editor = {P.~Wang}, publisher = {ACM} } @PhdThesis{Wi84, author = {F.~Winkler}, title = {The {C}hurch-{R}osser Property in Computer Algebra and Special Theorem Proving: An Investigation of Critical Pair Completion Algorithms}, school = {Universit\"at Linz}, year = 1984 } @PhdThesis{Wi89, author = {D.~Wi{\ss}mann}, title = {An\-wen\-dung von {R}e\-wri\-ting-{Techniken} in {polyzyklischen} {Gruppen}}, school = {Universit\"at Kaiserslautern}, year = 1989 } @InProceedings{ZhBl93, author = {A.~Zharkov and Yu.~Blinkov}, title = {Involution Approach to Solving Systems of Algebraic Equations}, booktitle = {Proc.~IMACS'93}, year = 1993, pages = {11-16} } @MastersThesis{Zi87, author = {M.~Zimnol}, title = {Bei\-spie\-le al\-ge\-bra\-ischer {R}e\-duk\-tions\-struk\-turen}, school = {Universit\"at Kaiserslautern}, year = 1987 } @MastersThesis{Za78, author = {G.~Zacharias}, title = {Generalized {G}r\"obner Bases in Commutative Polynomial Rings}, school = {M.~I.~T., Dept.~of Comp.~Sci.}, year = 1978 }