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TitleA generalization of Gröbner basis algorithms to polycyclic group rings
Author(s) Klaus Madlener, Birgit Reinert
TypeArticle in Journal
AbstractIt is well-known that for the integral group ring of a polycyclic group several decision problems are decidable, in particular the ideal membership problem. In this paper we define an effective reduction relation for group rings over polycyclic groups. This reduction is based on left multiplication and hence corresponds to left ideals. Using this reduction we present a generalization of Buchberger's Grobner basis method by giving an appropriate definition of "Grobner bases" in this setting and by characterizing them using the concepts of saturation and s-polynomials. The approach is extended to two-sided ideals and a discussion on a Grobner bases approach for right ideals is included.Copyright 1998 Academic Press Limited
Length21
ISSN0747-7171
File
URL dx.doi.org/10.1006/jsco.1997.0165
LanguageEnglish
JournalJournal of Symbolic Computation
Volume25
Number1
Pages23-43
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year1998
MonthJanuary
Translation No
Refereed No
Organization Universität des Saarlandes
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