The W-pure Submodule And Related Problems Pure Mathematics

Pure theorem and w-theorem have received a good deal of attention contin-uously in a number of literature. In this paper, Firstly, we apply the notion of pure theorem, w-module and its corresponding results to characterize the charac-terization of w-pure theorem, secondly, we introduce the concept of w-pure exact, w-pure submodule and w-pure factor module, We find the nature of w-pure sub-module and w-pure factor module, in order to find the different between w-pure submodule and w-pure factor module, We introduce some example and generalize some good results. Extending the nuture of w-pure submodule and w-pure factor module. In the end, we further introduce w-pure injective module and w-pure projective module, and these two groups to describe in detail, proof the link be-tween w-pure injective module and w-pure projective module, in addition, the introduction of the notion of w-pure semisimple ring, and proof in the context of w-pure semisimple ring, all the concepts in this paper has a close link between.