Gröbner bases in function rings—A guide for introducing reduction relations to algebraic structures

Gröbner bases as a means of studying ideals in polynomial rings have been generalized to other algebraic structures. The purpose of this paper is to present a general setting for Gröbner bases developed by the author in her habilitation thesis. This thesis was co-refereed by Volker Weispfenning who has contributed to the field of Gröbner bases in various publications.