Abstract
In this paper, we introduce and study the concepts of hollow – J–lifting modules and FI – hollow – J–lifting modules as a proper generalization of both hollow–lifting and J–lifting modules . We call an R–module M as hollow – J – lifting if for every submodule N of M with is hollow, there exists a submodule K of M such that M = K Ḱ and K N in M . Several characterizations and properties of hollow –J–lifting modules are obtained . Modules related to hollow – J–lifting modules are given .
Highlights
Orhan, Keskin and Tribak introduced the concept of hollow–lifting modules; An R–module is hollow – lifting if for every submodule N of M with is hollow, there exists a direct summand K ofM, such that K is a coessential submodule of N in M [1]
2) Every submodule N of M with is hollow can be written as N = K L, with K is a direct summand of M and L M
3) Every submodule N of M with is hollow can be written as N = K + L, with K is a direct summand of M and L M
Summary
Orhan , Keskin and Tribak introduced the concept of hollow–lifting modules; An R–module is hollow – lifting if for every submodule N of M with is hollow , there exists a direct summand K ofM, such that K is a coessential submodule of N in M [1]. Theorem (2.8) : An R–module M is hollow–J–lifting , if and only if for every submodule N of M with is hollow, N has J–supplement K in M such that K N is a direct summand of N.
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