Jacobson Radical Isomorphism Theorems for Mixed Modules Part One: Determining the Torsion

Abstract

Let R be a complete discrete valuation domain. A class of R-modules satisfies an isomorphism theorem if modules in that class are determined by their endomorphism rings. Do there exist classes of mixed R-modules for which the Jacobson radical of the endomorphism ring determines the structure of the modules? As a first step in answering this question, this article shows that there are two classes of mixed R-modules for which the Jacobson radical of the endomorphism ring determines the structure of the maximal torsion submodules of modules in that class.