S-Essentially Compressible Modulesand S-Essentially Retractable Modules

Abstract

Let R be a commutative ring with 1 and M be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) Modules. We study s-essentially compressible (s-essentially retractable). We give some of their advantages, properties, characterizations and examples. We also study the relation between s-essentially compressible (s-essentially retractable modules) and some classes of modules.