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.

Keywords:

• τ-comultiplication module
• τ-essential submodule
• τ-maximal ideal
• τ-pseudo-complement
• τ-simple module

2010 Mathematics Subject Classification:

• 13D30
• 16S90
• 18E40

Acknowledgements

The author would like to thank the referee for his/her valuable comments and suggestions to improve the presentation of this article.

Additional information

Funding

Trakya Üniversitesi.