Comultiplication modules relative to a hereditary torsion theory

Abstract

Let R be a commutative ring with identity and τ be a hereditary torsion theory on R-Mod. In this article, we introduce and study the concept of τ-comultiplication module. We present several properties and characterizations of τ-comultiplication modules. We also investigate modules for which every submodule has a unique τ-pseudo-complement and prove that every τ-comultiplication module is a module with unique τ-pseudo-complements.