Sum 2-Irreducible Submodules of a Module

Abstract

Let R be a commutative ring with identity and M be an R-module. M is said to be sum-irreducible precisely when it is non-zero and cannot be expressed as the sum of two proper submodules of itself. In this paper, we will introduce the concept of sum 2-irreducible submodules of M as a generalization of sum irreducible submodules of M and investigate some basic properties of this class of modules.

Key words and phrases. Sum irreducible submodule, 2-irreducible ideal, sum 2-irreducible submodule.

2000 Mathematics Subject Classification. 13C13, 13C99