Let be a commutative ring with 1 and left unitary . In this paper, the generalizations for notions of compressible module retractable are given. An is termed to semi-essentially if can embedded in every non-zero semi-essential submodules. module, submodule an Some their advantages characterizations examples We also study relation between these classes some other modules.

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

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We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...