Pu-visible Submodule with their most prominent characteristics

Abstract

In this article, the concept of pu-visible submodules of an S-module Y is introduced which is a generalization of the concept of visible submodule. Some charactrizations and properties are proven. Also the results of pu-visible submodule by a module Y will by presented by giving many results and properties that explain and discuss that concept, one of the most important of them show that the submodule of Y is pu-visible when the residual of it is pu-visible ideal of S and the opposite is achieved. In addition to many results that have been presented.