Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …

Let $ R $ be a commutative ring with unity $(1\not= 0) $ and let $\mathfrak {J}(R) $ be the set
of all ideals of $ R $. Let $\phi:\mathfrak {J}(R)\rightarrow\mathfrak {J}(R)\cup\{\emptyset\} …

The concept of essential submodules is a well known concept. In this paper we try to replace
an arbitrary submodule of M, say T, instead of 0 in the definition of essential submodules. By …

Let be a commutative ring with identity and let be an R-module. We call an R-submodule of
as P-essential if for each nonzero prime submodule of and 0. Also, we call an R-module as …

Let $ R $ be a commutative ring with nonzero identity and $ n $ be a positive integer. In this
paper, we study the concepts of $ n $-absorbing $\delta $-primary ideals and weakly $ n …

A left R-module M is called weakly prime module if the annihilator of any nonzero
submodule of M is a prime ideal and a proper submodule P of M is called weakly prime …

Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a
class of modules which is an analogous of δ-supplemented modules defined by Kosan. The …

Let $ R $ be a commutative ring with identity‎.‎ A proper ideal $ P $ of $ R $ is a< n> $(n-1, n)
$-$\Phi_m $-prime ($(n-1, n) $-weakly prime) ideal if $ a_1,\ldots, a_n\in R $‎,‎ $ a_1\cdots …

Let R be a ring and M a right R‐module with S= End (MR). The module M is called almost
principally quasi‐injective (or APQ‐injective for short) if, for any m∈ M, there exists an S …

This article introduces and advances the basic theory of “uniformly primary ideals” for
commutative rings, a concept that imposes a certain boundedness condition on the usual …