In this paper, we introduce the notion of P-coretractable module . Some basic properties of this class of modules are investigated and some relationships between these modules and other related concepts are introduced . Also , we give the notion of strongly P-coretractable and study it comparison with P-coretractable , moreover the mono-P-coretractable concept are introduced and studied .
A new generalizations of retractable modules relative to a submodule are introduced where a module ℳ is called retractable module relative to a submodule N of M if for all non-zero submodule K of ℳ such that contains N, there exists a non-zero homomorphism f∈Hom(ℳ, K). Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied.
In this paper, we introduce two new notions related with coretrectable modules which are called essentially coretrectable and weakly essentially coretrectable modules. Some basic properties of these classes are investigated and some relationships between these modules and other related concepts are given.
Let R be a ring with identity and M be an R-module with unity. In this paper we introduce the notion of C-coretractable modules. Some basic properties of this class of modules are investigated and some relationships between these modules and other related concepts are introduced. Also, we give the notion of strongly C-coretractable and study it comparison with C-coretractable.
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