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 …

A proper submodule N of a module M over a ring R is said to be prime (or P-prime) if re e N
for re R and ee M implies that either ee N or re P= N: M. In other words, N is a prime …

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 …

Let R be a commutative ring with 1 and M be a (left) unitary R–module. This essay gives
generalizations for the notions prime module and some concepts related to it. We termed an …

‎ Let $ R $ be a commutative ring with identity‎,‎ $ S $ a multiplicatively closed subset of $ R $‎,‎
and $ M $ be an $ R $-module‎.‎ The goal of this work is to introduce the notion of $ S $-pure …

Let R be a commutative ring and M be an R-module. We say that M is fully primary, if every
proper submodule of M is primary. In this paper, we state some characterizations of fully …

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 …

Let R be a commutative ring and M be an R-module. We say that M is (almost) fully primary,
if every (nonzero) proper submodule of M is primary. In this paper, we state some …

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 …

We provide the notion of strongly semiprime submodules of a given right $ R $-module $ M
$ and describe properties of them as a generalization of completely semiprime ideals in …