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TitleGroebner Bases in non-Commutative Reduction
Author(s) Klaus Madlener, Birgit Reinert
TypeArticle in Journal
AbstractGröbner bases of ideals in polynomial rings can be characterized by properties of reduction relations associated with ideal bases. Hence reduction rings can be seen as rings with reduction relations associated to subsets of the ring such that every finitely generated ideal has a finite Gröbner basis. This paper gives an axiomatic framework for studying reduction rings including non-commutative rings and explores when and how the property of being a reduction rings is preserved by standard ring constructions such as quotients and sums of reduction rings, and polynomial and monoid rings over reduction rings.
PublisherCambridge University Press
EditorB.Buchberger and F. Winkler
Translation No
Refereed No
Conferencename33 Years of Groebner Bases