RINGS CHARACTERIZED BY THEIR FUZZY SUBMODULES

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we i ntroduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-m odule. We establish their basic properties, and use them to obtain fuz zy theoretic characterizations of right weakly regular rings. Among ot her results, we prove that a ring R is right weakly regular if and onl y if each fuzzy submodule of a cyclic R-module is pure fuzzy.