Abstract:
Gröbner 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.

Klaus Madlener, Birgit Reinert
Fachbereich Informatik
Postfach 3049
67653 Kaiserslautern, Germany