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Bibliography

Ap88
J.Apel, Gröbnerbasen in nichtkommutativen Algebren und ihre Anwendung PhD Thesis. Leipzig. 1988.

ApLa88
J. Apel and W. Lassner. An Extension of Buchberger's Algorithm and Calculations in Enveloping Fields of Lie Algebras. Journal of Symbolic Computation(1988) 6. pp 361-370.

Ap95
J. Apel. A Gröbner Approach to Involutive Bases. Journal of Symbolic Computation(1995) Vol. 19 No. 5. pp 441-457.

AvMa84
J. Avenhaus and K. Madlener. The Nielsen Reduction and P-Complete Problems in Free Groups. Theoretical Computer Science 32(1984). pp 61-76.

AvMaOt86
J. Avenhaus, K. Madlener, F. Otto. Groups Presented by Finite Two-Monadic Church-Rosser Thue Systems. Transactions of the American Mathematical Society. Vol. 297(1986). pp 427-443.

BaGa94a
L. Bachmair and H. Ganzinger. Rewrite-Based Equational Theorem Proving With Selection Simplification. Journal of Symbolic Computation(1994) Vol. 4 No. 3. pp 1-31.

BaGa94b
L. Bachmair and H. Ganzinger. Buchberger's algorithm: A constraint-based completion procedure. Proc. CCL'94. pp 285-301.

Ba81
G. Bauer. Zur Darstellung von Monoiden durch konfluente Reduktionssysteme. PhD Thesis. Universität Kaiserslautern. 1981.

BaCaMi81
G. Baumslag, F. Cannonito and C. Miller III. Computable Algebra and Group Embeddings. Journal of Algebra 69(1981). pp 186-212.

BeWe92
T. Becker and V. Weispfenning. Gröbner Bases - A Computational Approach to Commutative Algebra. Springer Verlag(1992).

Bu65
B. Buchberger. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal. PhD Thesis. Universität Innsbruck. 1965.

Bu83
B. Buchberger. A Critical-Pair Completion Algorithm for Finitely Generated Ideals in Rings. Proc. Logic and Machines: Decision Problems and Complexity. Springer LNCS 171. pp 137-161.

Bu85
B. Buchberger. Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory. N. K. Bose (ed). Multidimensional Systems Theory. Chapter 6. 1985. Dordrecht: Reidel. pp 184-232.

Bu87
B. Buchberger. Applications of Gröbner Bases in Non-Linear Computational Geometry. In: R. Janßen (ed.). Trends in Computer Algebra. Springer LNCS 296(1987). pp 52-80.

Bu91
R. Bündgen. Simulating Buchberger's Algorithm by a Knuth-Bendix Completion Procedure. Proc. RTA'91. pp 386-397.

BoOt93
R. Book and F. Otto. String-Rewriting Systems. Springer Verlag(1993).

CoLiOS92
D. Cox, J. Little and D. O'Shea. Ideals, Varieties, and Algorithms. Springer Verlag(1992).

CrOt94
R. Cremanns and F. Otto. Constructing Canonical Presentations for Subgroups of Context-Free Groups in Polynomial Time. Proc. ISSAC'94.

De12
M. Dehn. Über unendliche diskontinuierliche Gruppen. Mathematische Annalen 71(1912). pp 116-144.

De92
T. Deiß. Conditional Semi-Thue Systems for Presenting Monoids. Proc. STACS'92. pp 557-565.

FaFeGr93
D. Farkas, C. Feustel, E. Green. Synergy in the theories of Gröbner bases and path algebras. Canadian Journal of Mathematics. Vol. 45 Nr. 4(1993). pp 727-739.

Ga88
A. Galligo. Some algorithmic questions on ideals of differential operators. Proc. EUROCAL '85 II. LNCS 204 (1985). pp 413-421.

GeCzLa92
K. O. Geddes, S. R. Czapor and G. Labahn. Algorithms for Computer Algebra. Kluwer Academic Publishers. Massachusettes(1992).

Gi79
R. Gilman. Presentations of Groups and Monoids. Journal of Algebra 57(1979). pp 544-554.

Hi64
H. Hironaka. Resolution of singularities of an Algebraic Variety over a Field of Characteristic Zero. Annals of Mathematics 79(1964). pp 109-326.

Hu80
G. Huet. Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems. Journal of the ACM 27(4)(1980). pp 797-821.

Hu81
G. Huet. A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm. Journal of Computer and System Science 23(1)(1981). pp 11-21.

Ja81
M. Jantzen. On a Special Monoid with Single Defining Relation. Theoretical Computer Science 16(1981). pp 61-73.

Ja85
M. Jantzen. A Note on a Special One-rule Semi-Thue System. Information Processing Letters 21(1985). pp 135-140.

KaKa84
A. Kandri-Rody and D. Kapur. An Algorithm for Computing the Gröbner Basis of a Polynomial Ideal over an Euclidean Ring. Technical Information Series General Electric Company Corporate Research and Development Schenectady. NY 12345. Dec. 1984.

KaKa88
A. Kandri-Rody and D. Kapur. Computing a Gröbner Basis of a Polynomial Ideal over an Euclidean domain. Journal of Symbolic Computation 6(1988). pp 37-57.

KaKaWi89
A. Kandri-Rody, D. Kapur and F. Winkler. Knuth-Bendix Procedure and Buchberger Algorithm - a Synthesis. Proc. ISSAC'89. pp 55-67.

KaMe79
M. I. Kargapolov and Ju. I. Merzljakov. Fundamentals of the Theory of Groups. Springer Verlag(1979).

KaMa86
D. Kapur and K. Madlener. Private communication.

KaNa85a
D. Kapur and P. Narendran. Constructing a Gröbner Basis for a Polynomial Ring. Proc. Combinatorial Algorithms in Algebraic Structures. Otzenhausen(1985). Eds J. Avenhaus, K. Madlener. Universität Kaiserslautern.

KaNa85b
D. Kapur and P. Narendran. A Finite Thue System with Decidable Word Problem and Without Equivalent Finite Canonical System. Theoretical Computer Science 35(1985). pp 337-344.

KaWe90
A. Kandri-Rody and V. Weispfenning. Non-Commutative Gröbner Bases in Algebras of Solvable Type. Journal of Symbolic Computation 9(1990). pp 1-26.

Ke97
B. J. Keller. Alternatives in Implementing Noncommutative Gröbner Basis Systems. See this volume.

KnBe70
D. Knuth and P. Bendix. Simple Word Problems in Universal Algebras. J. Leech (editor). Computaional Problems in Abstract Algebra. Pergamon Press. Oxford. 1970. pp 263-297

Kr93
H. Kredel. Solvable Polynomial Rings. Verlag Shaker. Aachen. 1993.

KuMa89
N. Kuhn and K. Madlener. A Method for Enumerating Cosets of a Group Presented by a Canonical System. Proc. ISSAC'89. pp 338-350.

KuMaOt94
N. Kuhn, K. Madlener and F. Otto. Computing Presentations for Subgroups of Polycyclic Groups and of Context-Free Groups. Applicable Algebra in Engineering, Communication and Computing 5(1994). pp 287-316.

La85
W. Lassner. Symbol Representations of Noncommutative Algebras. Proc. EUROCAL'85. Springer LNCS 204. pp 99-115.

La76
M. Lauer. Kanonische Repräsentanten für die Restklassen nach einem Polynomideal. Diplomarbeit. Universität Kaiserslautern. 1976.

LeCh86
P. Le Chenadec. Canoniacl Forms in Finitely Presented Algebras. Pitman/Wiley. London. 1986.

LySch77
R. C. Lyndon and P. E. Schupp. Combinatorial Group Theory. Springer Verlag(1977).

Ma86
K. Madlener. Existence and Construction of Gröbner Bases for Ideals in Reduction Rings. Working paper. 1986.

MNOZ93
K. Madlener, P. Narendran, F. Otto and L. Zhang. On Weakly Confluent Monadic String-Rewriting Systems. Theoretical Computer Science 113(1993). pp 119-165.

MaOt89
K. Madlener and F. Otto. About the Descriptive Power of Certain Classes of Finite String-Rewriting Systems. Theoretical Computer Science 67(1989). pp 143-172.

MaOt94
K. Madlener and F. Otto. Some Undecidability Results for Finitely Generated Thue Congruences on a Two-Letter Alphabet. E. Schock (ed.). Beiträge zur Angewandten Analysis und Informatik, Helmut Brakhage zu Ehren. Verlag Shaker. Aachen. 1994. pp 248-261.

MaRe93a
K. Madlener and B. Reinert. On Gröbner Bases in Monoid and Group Rings. SEKI Report SR-93-08. Universität Kaiserslautern.

MaRe93b
K. Madlener and B. Reinert. Computing Gröbner Bases in Monoid and Group Rings. Proc. ISSAC'93. pp 254-263.

MaRe95
K. Madlener and B. Reinert. On Gröbner Bases for Two-Sided Ideals in Nilpotent Group Rings. SEKI Report SR-95-01. Universität Kaiserslautern.

MaRe96a
K. Madlener and B. Reinert. A Generalization of Gröbner Bases Algorithms to Nilpotent Group Rings. Applicable Algebra in Engineering, Communication and Computing Vol. 8 No. 2(1997). pp 103-123.

MaRe97a
K. Madlener and B. Reinert. A Generalization of Gröbner Basis Algorithms to Polycyclic Group Rings. Journal of Symbolic Computation. To appear.

MaRe97b
K. Madlener and B. Reinert. Congruemces in Monoids and Ideals in Monoid Rings. Technical Report. Universität Kaiserslautern. 1997.

MaKaSo76
W. Magnus, A. Karrass and D. Solitar. Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations. Dover Publications. New York. 1976.

Mar93
C. Marché. Normalized Rewriting - Application to Ground Completion and Standard Bases. In: H. Comon, J.-P. Jouannaud (Eds.). Term Rewriting. Springer. 1993. pp 154-169.

Mo85
F. Mora. Gröbner Bases for Non-Commutative Polynomial Rings. Proc. AAECC-3(1985). Springer LNCS 229. pp 353-362.

Mo88
T. Mora. Gröbner bases for non-commutative algebras. Proc. ISSAC'88. LNCS 358(1989). pp 150-161.

Mo94
T. Mora. An Introduction to Commutative and Non-Commutative Gröbner Bases. Theoretical Computer Science 134(1994). pp 131-173.

Ni21
J. Nielsen. Om Regning med ikke kommutative Faktoren og dens Anvendelse i Gruppeteorien. Mat. Tidsskr. B.(1921). pp 77-94.

OD83
C. Ó'Dúnlaing. Undecidable Questions Related to Church-Rosser Thue Systems. Theoretical Computer Science 23(1983). pp 339-345.

Ot87
F. Otto. On Deciding the Confluence of a Finite String-Rewriting System on a Given Congruence Class. Journal of Computer and System Science 35(1987). pp 285-310.

OtZh91
F. Otto and L. Zhang. Decision Problems for Finite Special String-Rewiting Systems that are Confluent on some Congruence Class. Acta Informatica 28(1991). pp 477-510.

Pa85
L. Pan. On the Gröbner Bases of Ideals in Polynomial Rings over a Prinicipal Ideal Domain. University of California. Santa Barbara. Department of Mathematics. Internal Manuscript. 1985.

Pe97
M. Pesch. Two-sided Gröbner Bases in Iterated Ore Extensions. See this volume.

Re95
B. Reinert. Gröbner Bases in Monoid and Group Rings. PhD Thesis. Universität Kaiserslautern. 1995.

Re96
B. Reinert. Introducing Reduction to Polycyclic Group Rings - A Comparison of Methods. Reports on Computer Algebra No 9. Centre of Computer Algebra. Universität Kaiserslautern. 1996.

Ro93
A. Rosenmann. An Algorithm for Constructing Gröbner and Free Schreier Bases in Free Group Algebras. Journal of Symbolic Computation 16(1993). pp 523-549.

Sa91
A. Sattler-Klein. Divergence Phenomena During Completion. Proc. RTA'91. pp 374-385.

Sa96
A. Sattler-Klein. A Systematic Study of Infinite Canonial Systems generated by Knuthe-Bendix Completion and Related Problems. PhD Thesis. Universität Kaiserslautern. 1996.

Si87
C. Sims. Verifying Nilpotence. Journal of Symbolic Computation 3(1987). pp 231-247.

Si90
C. Sims. Implementing the Baumslag-Cannonito-Miller Polycyclic Quotient Algorithm. Journal of Symbolic Computation 9(1990). pp 707-723.

Si94
C. Sims. Computation with finitely presented groups. Cambridge University Press 1994.

Sq87
C. Squier. Word Problems and a Homological Finiteness Condition for Monoids. Journal of Pure Applied Algebra 49(1987). pp 201-217.

St85
S. Stifter. Computation of Gröbner Bases over the Integers and in General Reduction Rings. Diplomarbeit. Johannes Kepler Universität Linz. 1985.

St87
S. Stifter. A generalization of Reduction Rings. Journal of Symbolic Computation 4(1987). pp 351-364.

St90
T. Stokes. Gröbner Bases in Exterior Algebras. Journal of Automated Reasoning 6(1990). pp 233-250.

We87
V. Weispfenning. Gröbner Basis for Polynomial Ideals over Commutative Regular Rings. Proc. EUROCAL'87. Springer LNCS 378. pp 336-347.

We92
V. Weispfenning. Finite Gröbner Bases in Non-Noetherian Skew Polynomial Rings. Proc. ISSAC'92. pp 329-334.

Wi88
D. Wißmann. Applying Rewriting Techniques to Groups with Power-Commutation-Presentations. Proc. ISSAC'88. pp 378-389.

Wi89
D. Wißmann. Anwendung von Rewriting-Techniken in polyzyklischen Gruppen. PhD Thesis. Universität Kaiserslautern. 1989.

ZhBl93
A. Zharkov and Yu. Blinkov. Involution Approach to Solving Systems of Algebraic Equations. Proc. IMACS'93. pp 11-16.


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