Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between a given module extension submodules. The two modules direct product their quotient are studied investigated.

Abstract : In this paper we study the properties of the finite topology on the dual of a module over an arbitrary ring. We aim to give conditions when certain properties of the field case can still be found here. Investigating the correspondence between the closed submodules of the dual M∗ of a module M and the submodules of M , we prove some characterizations of PF rings: the up stated corresp...

Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

In F. Caselli (Involutory reflection groups and their models, J. Algebra 24:370–393, 2010), a uniform Gelfand model is constructed for all nonexceptional irreducible complex reflection groups which are involutory. Such models can be naturally decomposed into the direct sum of submodules indexed by Sn-conjugacy classes, and we present here a general result that relates the irreducible decomposit...

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 introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...