On essential-prime sub-modules

摘要

Let S be a commutative ring with identity, let A be an until (left) S-module. In this paper, we study the concepts : essential prime sub-modules as a generalization of prime sub-modules. A sub-module H of an S-module A is said to be essential-prime if whenever ri is an element of Si, a is an element of A with <= and rai is an element of Hi theni eitheri a is an element of Hi or ri is an element of H : iA. We give a number of basic properties and characterizations for this type of sub-modules.