Let M be a left R-module. In this paper a generalization of the notion of m-system set of rings
to modules is given. Then for a submodule N of M, we define\sqrt p N:= m ε M: every m …

Let $ _RU $ be a left R-module whose Morita context is nondegenerate and $ S={\text
{End}}(U) $. We show the following:(1) There is a projectivity (that is, an order-preserving …

The submodule ZM/D ¹x 2 M j xI D 0 for an essential right ideal I of Rº of a right module M
over a ring R is the singular submodule of M. The module M is non-singular if ZM/D 0; it is …

In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …

Abstract Let\(R\) be a ring and\(\tau\) be a preradical for the category of left\(R\)-modules. In
this paper, we study on modules whose maximal submodules have\(\tau\)-supplements. We …

In this paper, we introduce and study ℙ-radical and 𝕄-radical modules over commutative
rings. We say that an 𝑅-module 𝑀 is ℙ-radical whenever 𝑀 satisfies the equality (PM p: M) …

Let S be a commutative ring with identity, let A be an until (left) S-module. In this paper, we
study the concepts: essential prime sub-modules as a generalization of prime sub-modules …

Rings whose finitely generated modules are extending Page 1 JOURNAL OF PURE AND
Journal of Pure and Applied Algebra 111 (1996) 325-328 APPLIED ALGEBRA Rings whose …

Let M and P be right R− modules. A submodule K of an R− module M is called P− dense if
for each m∈ M,(K: m) is a P− faithful right ideal of R. PR is nonsingular if and only if, for each …

Let R be a commutative ring. We determine the cyclic modules in the projectivity domain and
those in the injectivity domain of a simple R-module. An R-module M is called poor (p-poor) …