Klaus Madlener and Birgit Reinert. Relating rewriting techniques on monoids and rings: congruences on monoids and ideals in monoid rings. Theoret. Comput. Sci., 208(1-2):3--31, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Grobner bases and rewriting systems, as well as the theorem (Theorem 1.7) connecting these two concepts. For further information about rewriting systems see [11] for a more detailed account of noncommutative Grobner bases see [4] and [9] and for the connections between these topics see [7]. We begin with rewriting systems. Definition 1.1 (Division ordering) Let A be a finite set and let A # be the collection of all (noncommutative) words, including the empty word, over the alphabet A. A division ordering on A # is a partial ordering which is well founded and compatible with ....

Klaus Madlener and Birgit Reinert. Relating rewriting techniques on monoids and rings: congruences on monoids and ideals in monoid rings. Theoret. Comput. Sci., 208(1-2):3--31, 1998.

....where, for i 2 [1; k] c i 2 Knf0g and u i 2 hXi, then Can(f; I; is computed in O(kmd 2 ) arithmetical operations, where m : maxfL(u i ) j i 2 [1; k]g. y In the non commutative case, the notion of (left) Border basis essentially coincides with the one of prefix Grobner basis introduced in [MR] and [R] In the commutative case, it is strictly related with the notion of Janet basis introduced by Zharkov (cf. Z] the papers quoted there and also [Ap] as a generalization of Janet s theory ( J] of partial differential equations. Borges, Borges, Mora Proof. Following [FGLM] we store ....

....of Can(us; I; in 1.8.i, when the binomial ideal I is generated by binomials having the form s Gamma t, does not involve in fact arithmetical operations; its complexity is rather characterized by L(u) reduction steps. This kind of ideals is strongly related to monoid presentations (cf. [MR] for a recent study regarding this relation) We also remark that in the same mood FGLM algorithm has been used in [RMM] in their interpretation of Todd Coxeter Algorithm in terms of Grobner techniques. 2. FGLM algorithm for free associative algebras In this section we present our ....

[Article contains additional citation context not shown here]

Madlener K., Reinert B. (199?). "Relating Rewriting Techniques on Monoids and Rings: Congruences on Monoids and Ideals in Monoid Rings." Theoretical Computer Science. To appear.

.... fact that they can be presented as string rewriting systems and, hence, completion based procedures a la Knuth and Bendix can be applied [11] Recently, some authors have started using Grobner basis methods to model groups in appropriate rings and solve group theoretical problems in this setting [16, 4]. In [16] the existence of explicit connections is proved ffl between the word problem for monoids and the ideal membership problem for free monoid rings; ffl between the word problem for groups and the ideal membership problem for free group rings; ffl between the submonoid problem and the ....

.... can be presented as string rewriting systems and, hence, completion based procedures a la Knuth and Bendix can be applied [11] Recently, some authors have started using Grobner basis methods to model groups in appropriate rings and solve group theoretical problems in this setting [16, 4] In [16] the existence of explicit connections is proved ffl between the word problem for monoids and the ideal membership problem for free monoid rings; ffl between the word problem for groups and the ideal membership problem for free group rings; ffl between the submonoid problem and the subalgebra ....

[Article contains additional citation context not shown here]

K. Madlener and B. Reinert. Relating rewriting techniques on monoids and rings: Congruences on monoids and ideals in monoid rings. Theoretical Computer Science, to appear.

....monoid and group rings. The theoretical background on prefix Grobner bases for monoid and group rings was first presented at ISSAC 93 by Madlener and Reinert in [10] Different specialized definitions of reduction relations followed [19, 14, 11, 12] Applications of these methods can be found in [15] where connections are presented ffl between the word problem for monoids and the ideal membership problem for free monoid rings; ffl between the word problem for groups and the ideal membership problem for free group rings; ffl between the submonoid problem and the subalgebra problem for ....

K. Madlener and B. Reinert. Relating rewriting techniques on monoids and rings: Congruences on monoids and ideals in monoid rings. Theoretical Computer Science, to appear.

....[6] The next step of generalizing Grobner bases was to study arbitrary monoid and group rings. The theoretical background on prefix Grobner bases was first presented at ISSAC 93 by Madlener and Reinert in [9] Different specialized definitions of reduction relations followed [15, 11, 10, 12] In [13] connections between the word problem for monoids and groups and the ideal membership problem in free monoid and free group rings, respectively, as well as connections between the submonoid problem and the subalgebra problem and between the subgroup problem and the onesided ideal membership ....

....to continue or to interrupt the computation after each newly computed prefix Grobner basis, or without user interaction in batch mode. Statistical information concerning memory consumption and run time are provided, too. They allow assessments on the efficency of the procedures implemented. In [13] connections between the word problem for monoids and groups and the ideal membership problem in free monoid and free group rings, respectively, as well as connections between the submonoid problem and the subalgebra problem and between the subgroup problem and the onesided ideal membership ....

[Article contains additional citation context not shown here]

K. Madlener, B. Reinert. Relating rewriting techniques on monoids and rings: Congruences on monoids and ideals in monoid rings. TCS, 1998.

.... fact that they can be presented as string rewriting systems and, hence, completion based procedures a la Knuth and Bendix can be applied [12] Recently, some authors have started using Grobner basis methods to model groups in appropriate rings and solve group theoretical problems in this setting [17, 4]. In [17] the existence of explicit connections between the word problem for monoids and groups and the ideal membership problem in free monoid and free group rings, respectively, as well as connections between the submonoid problem and the subalgebra problem and between the subgroup problem and ....

.... they can be presented as string rewriting systems and, hence, completion based procedures a la Knuth and Bendix can be applied [12] Recently, some authors have started using Grobner basis methods to model groups in appropriate rings and solve group theoretical problems in this setting [17, 4] In [17] the existence of explicit connections between the word problem for monoids and groups and the ideal membership problem in free monoid and free group rings, respectively, as well as connections between the submonoid problem and the subalgebra problem and between the subgroup problem and the ....

[Article contains additional citation context not shown here]

K. Madlener and B. Reinert. Relating rewriting techniques on monoids and rings: Congruences on monoids and ideals in monoid rings. Theoretical Computer Science, to appear.

No context found.

K. Madlener and B. Reinert. Relating rewriting techniques on monoids and rings: Congruences on monoids and ideals in monoid rings. September 1997.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC