The purpose of this paper and its sequel, is to introduce a new class of modules over a
commutative ring $ R $, called $\mathbb {P} $-radical modules (modules $ M $ satisfying the …

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 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 …

Abstract We present $* $-primary submodules, a generalization of the concept of primary
submodules of an $ R $-module. We show that every primary submodule of a Noetherian …

Let M be a left R-module. A proper submodule P of M is called classical prime if for all ideals
and for all submodules N⊆ M, implies that or. We generalize the Baer–McCoy radical (or …

In this paper, we investigate radical Noetherian modules as a collection of modules whose
lattice of radical submodules is Noetherian. The collection of radical Noetherian modules …

Let R be a commutative ring with identity. The purpose of this paper is to introduce and to
study a new class of modules over R called quasi-primaryful R-modules. This class contains …

This expository note delves into the theory of projective modules parallel to the one
developed for injective modules by Matlis. Given a perfect ring $ R $, we present a …

The notion of $ R $-regular module is introduced. We will show that if $ M $ is a torsion-free
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …

We prove that a commutative ring R is an artinian principal ideal ring if and only if the ring is
semilocal and every Rad-supplemented R-module is a direct sum of w-local R-modules …