Survey on second submodules of modules over commutative rings

TL;DR

This survey compiles and reviews research on second submodules of modules over commutative rings, highlighting their properties and significance in module theory.

Contribution

It provides a comprehensive collection of existing results on second submodules, serving as a valuable resource for future research in this area.

Findings

Extensive properties of second submodules are summarized.

The survey highlights the importance of second submodules in module theory.

Research trends and open problems are discussed.

Abstract

Let R be a commutative ring with identity. The concept of second submodule of an R-module (as a dual notion of prime submodules) was introduced and studied by S.Yassemi in 2001. This notion has obtained a great attention by many authors and now there is a considerable amount of research concerning this class of modules. The main purpose of this paper is to collect these results and provide a useful source for those who are interested in research in this field.