Notes on the Union of Weakly Primary Submodules

Abstract

Let R be a commutative ring with identity, and let M be an R-module. A proper submodule N of M is said to be weakly primary if 0≠rm∈N for r∈R and m∈M, which implies that either m∈N or rnM⊆N for some positive integer n. In this paper, we study weakly primary submodules, and we investigate the union of weakly primary submodules of R-modules.