Rings Whose CS Modules Are Countably Σ-CS

Abstract

A module M is called a CS module if every submodule of M is essential in a direct summand of M. In this paper, among other results, we prove that for a ring R with finitely generated right socle the following are equivalent: i) For every CS right R-module M, M ^(ℕ) is CS; ii) R is a right artinian ring with all uniforms Σ-quasi-injective.

Key Words:

• CS module
• Quasi-injective
• Continuous

Acknowledgment

The author wishes to express his gratitude to professors D. V. Huynh and S. K. Jain for very helpful suggestions and motivating discussions.