Title  Groebner Rings and Modules 
Author(s)  Bruno Buchberger 
Type  Article in Conference Proceedings 
Abstract  We 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. 
Keywords  axiomatic approach to Groebner bases theory, least common reducibles 
Length  4 
File 

Language  English 
Pages  2225 
Year  2001 
Annote  20011002A 
Note  RISCLinz Report Series No. 0120 
Editor  S. Maruster and B. Buchberger and V. Negru and T. Jebelean 
Translation 
No 
Refereed 
Yes 
Organization 
University of the West Timisoara 