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Let be a commutative ring with 1 and be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) module. As well as, we study closed (St-closed) compressible and closed (St-closed) retractable. Furthermore, some of their advantages, properties, categorizations and instances have been given. Finally, we study the relation between them.
Hakeem et al. (Tue,) studied this question.