Let $ N $ be a submodule of a module $ M $ and a minimal primary decomposition of $ N $
is known‎.‎ A formula to compute Baer's lower nilradical of $ N $ is given‎.‎ The relations …

In this note, we will make an intensive study of the notion of primal submodules of a module
over a commutative ring with identity. First, a number of results concerning of primal …

We introduce the notion of a strongly prime near-ring module and then characterize strongly
prime near-rings in terms of strongly prime modules. Furthermore, we define a T-special …

We introduce and study the concept of D-essential submodules and its dual concept, F-small
submodules, where D and F are arbitrary submodules of a module M. These two notions are …

Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose
of this paper is to investigate some new results (up to our knowledge) on the concept of semi …

Let R be a commutative ring with a nonzero identity and let M be a unitary R-module. We
introduce the concepts of 2-absorbing and weakly 2-absorbing submodules of M and give …

Throughout this note R is commutative ring with identity, and X be a left unitary R-module. A
proper submodule K of an R-module X is called nearly prime, if whenever implies that either …

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let S (M)
be the set of all submodules of M and ${\phi}: S (M){\rightarrow} S (M){\cup}\{{\emptyset}\} …

Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime
submodule of M is defined. It is shown that this notion of prime submodule inherits most of …

In this paper, we introduce a new concept named St-polyform modules, and show that the
class of Stpolyform modules is contained properly in the well-known classes; polyform …