journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-1631 Semi-essentially prime modules Al-Hakeem Mohammed Baqer Hashim Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq Al-Mothafar Nuhad S. Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq 26 6 1725 1730 01 06 2023

Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

 Prime module Semi-essentially compressible module Essentially compressible module Fully prime module Semi-uniform module access open retracted no