Specialization of modules

Abstract

Let R be a polynomial ring over k(u), where k is a field k and u is a finite family or inderterminates. The paper introduces the specialization of an arbitrary finitely generated R-module by the substitution of u to elements of k. This definition does not depend on the presentation of the given module and preserves basic properties and operations on modules (e.g. annihilator, dimension, Ext and Tor) for almost all specializations.