Date: Wed 19 Mar
Time: 15.00
Place: room 713 (seminario di Algebra e Geometria)

Speaker: Prof. Birgit Reinert, (Univ. Kaiserslautern)
Title: On Groebner Bases in Monoid and Group Rings
Reference: Teo Mora

Abstract. Groebner Bases, as introduced by Bruno Buchberger, allow to solve algebraic problems in commutative polynomial rings by means of reduction. In this talk we present a generalization of Groebner bases for finitely generated monoid and group rings. Reduction methods are used to represent the monoid elements as well as to descibe right ideal congruences in the respective rings. Since in general monoids do not allow admissible orderings, in defining suitable reduction relations serious problems arise: on one hand it is difficult to guarantee termination for reduction relations, and on the other hand, reduction does not necessarily capture the right ideal congruence. For special classes of monoids ( e.g. finite, commutative or free )and groups ( e.g. finite, free, plain, context-free, or polycyclic ) finite Groebner bases can be characterized and computed. These results will be presented here.