St-closed Submodule

Abstract

Throughout this paper R represents commutative ring with identity and M is a unitary left R- module, the purpose of this paper is to study a new concept, (up to our knowledge), named St- closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties