Modules in which pure submodule is essential in a direct summand
Commutative Algebra
2022-09-12 v1 Rings and Algebras
Abstract
In this paper, we study the class of modules have the property that every pure submodule is essential in a direct summand. These modules are termed as pure extending modules which is a proper generalisation of extending modules. Examples and counterexamples are given. We study some properties of pure extending modules and characterize regular ring, semisimple ring, local ring and PDS ring in terms of pure extending modules.
Cite
@article{arxiv.2209.04176,
title = {Modules in which pure submodule is essential in a direct summand},
author = {Kaushal Gupta and Shiv Kumar and Ashok Ji Gupta},
journal= {arXiv preprint arXiv:2209.04176},
year = {2022}
}