Introducing Reduction to Polycyclic Group Rings - A Comparison of Methods

  • t is well-known that for the integral group ring of a polycyclic group several decision problems are decidable. In this paper a technique to solve themembership problem for right ideals originating from Baumslag, Cannonito and Miller and studied by Sims is outlined. We want to analyze, how thesedecision methods are related to Gröbner bases. Therefore, we define effective reduction for group rings over Abelian groups, nilpotent groups and moregeneral polycyclic groups. Using these reductions we present generalizations of Buchberger's Gröbner basis method by giving an appropriate definition of"Gröbner bases" in the respective setting and by characterizing them using concepts of saturation and s-polynomials.

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Author:Birgit Reinert
URN (permanent link):urn:nbn:de:hbz:386-kluedo-4499
Serie (Series number):Reports on Computer Algebra (ZCA Report) (9)
Document Type:Preprint
Language of publication:English
Year of Completion:1996
Year of Publication:1996
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Gröbner bases; polycyclic group rings; rewriting
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011