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TitleGroebner Rings and Modules
Author(s) Bruno Buchberger
TypeArticle in Conference Proceedings
AbstractWe sketch an axiomatic approach for the theory of Groebner bases in rings and modules.

A Groebner ring is a ring with three additional operations: a Noetherian ordering, a ring quotient, and an operation called "least common reducible". In an earlier paper (1985) we had introduced axioms for slightly more complicated additional operations and we pose the problem of finding appropriate axioms for the above three operations in order to guarantee that

- a ring satisfying the axioms allow the construction of Groebner bases by considering finitely many least common reducibles and

- the axioms are preserved if one goes from a ring to the polynomial ring over the given ring and to various other rings that can be constructed from the given ring by various constructive functors.
Keywordsaxiomatic approach to Groebner bases theory, least common reducibles
NoteRISC-Linz Report Series No. 01-20
EditorS. Maruster and B. Buchberger and V. Negru and T. Jebelean
Translation No
Refereed Yes
Organization University of the West Timisoara