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TitleA Generalization of Gröbner Basis Algorithms to Nilpotent Group Rings
Author(s) Klaus Madlener, Birgit Reinert
TypeArticle in Journal
AbstractIt is well-known that for the integral group ring of a polycyclic-by-finite group several decision problems including the membership problem for right ideals are decidable. In this paper we define an effective reduction for group rings over finitely generated nilpotent groups -- a subclass of polycyclic-by-finite groups. Using this reduction we present a generalization of Buchberger's Gröbner basis method by giving an appropriate definition of "Gröbner bases" in this setting and by characterizing them using the concepts of saturation and s-polynomials. Our approach allows to compute such Gröbner bases by completion based algorithms and to use these bases to solve the membership problem for right and two-sided ideals in finitely generated nilpotent group rings using Gröbner basis algorithms and reduction.
KeywordsGröbner bases, Nilpotent group rings, Rewriting
JournalApplicable Algebra in Engineering, Communication and Computing
PublisherSpringer-Verlag GmbH
Translation No
Refereed No
Organization Universität Kaiserslautern