Abstract
Throughout this note, R is commutative ring with identity and M is a unitary R-module. In this paper, we introduce the concept of quasi J- submodules as a – and give some of its basic properties. Using this concept, we define the class of quasi J-regular modules, where an R-module J- module if every submodule of is quasi J-pure. Many results about this concept
Highlights
In section one we introduce a comprehensive study of J-pure submodules
Submodule is quasi J-pure. be a Z-module, and N = (̅ ̅) = {(̅ ̅),. It is that N is quasi J-pure submodule of, since for each and there exists a
But B is a submodule in N, so there exists a J-pure submodule L in N such that B L and
Summary
A submodule N of an R-module is called pure in M if for every ideal I of R [1]. L, and an R-module is called quasi – regular module if every submodule of is quasi – pure [4]. We introduce the concept of quasi J- submodule. A submodule of is called a quasi J- submodule of if for each and N, there exists a J- submodule L of such that N L and L. submodule is quasi J-pure. Be a Z-module, and N = (̅ ̅) = {(̅ ̅), It is that N is quasi J-pure submodule of , since for each and there exists a. Since is quasi J-pure in , there exists a J-pure submodule L of such that.
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