Related papers: S-1-absorbing primary submodules

As an alternative perspective on the injectivity of a pure-injective module, a pure-injective module M is said to be pi-indigent if its subinjectivity domain is smallest possible, namely, consisting of exactly the absolutely pure modules. A…

Let $R$ be a (commutative Noetherian) local ring of prime characteristic that is $F$-pure. This paper studies a certain finite set ${\mathcal I}$ of radical ideals of $R$ that is naturally defined by the injective envelope of the simple…

Let $R$ be a commutative unital ring and $N$ be a submodule of an $R$-module $M$. The submodule $\langle E_M(N)\rangle$ generated by the envelope $E_M(N)$ of $N$ is instrumental in studying rings and modules that satisfy the radical…

For an $R$-module $M$, projective in $\sigma[M]$ and satisfying ascending chain condition (ACC) on left annihilators, we introduce the concept of Goldie module. We also use the concept of semiprime module defined by Raggi et. al. in…

This paper gives generalization of a notion of supplemented module. Here, we utilize some algebraic properties like supplemented, amply supplemented and local modules in order to obtain the generalization. Other properties that are…

This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the ring $\mathbb{Z}[x]$ of polynomials in one variable. We…

Let R be a commutative ring with unity and M be an R-module. In this study, we construct the \tilde{Spec}(M) topology using the prime spectrum of module M and multiplicatively closed subsets of R with the closed sets \tilde{V}(S)={P \in…

In this paper, we introduce a new concept in Nil-semicommutative modules and present it as an extension of Nil-semicommutative rings to modules. We prove that the class of Nil-semicommutative modules is contained in the class of Weakly…

In this paper, we introduce the concept of centrally endo-AIP modules. We call a module M centrally endo-AIP, if the left annihilator of any fully invariant submodule N of M in the endomorphism ring S = End(M) is a centrally s-unital ideal…

In [24], Yassine et al. introduced the notion of 1-absorbing prime ideals in commutative rings with nonzero identity. In this article, we examine the concept of 1-absorbing prime elements in C-lattices. We investigate the C-lattices in…

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we introduce and study the notions of $S$-pure $S$-exact sequences and $S$-absolutely pure modules which extend the classical notions of pure…

Let R be a Krasner (m,n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. Several properties and…

Given a multiplicative subset $S$ in a commutative ring $R$, we consider $S$-weakly cotorsion and $S$-strongly flat $R$-modules, and show that all $R$-modules have $S$-strongly flat covers if and only if all flat $R$-modules are…

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their underlying monoid congruences. These mesoprimary…

Let $R$ be a commutative ring. We investigate $R$-modules which can be written as \emph{finite} sums of {\it {second}} $R$-submodules (we call them \emph{second representable}). We provide sufficient conditions for an $R$-module $M$ to be…

Here we introduce and characterize a new class of le-modules $_{R}M$ where $R$ is a commutative ring with $1$ and $(M,+,\leqslant,e)$ is a lattice ordered semigroup with the greatest element $e$. Several notions are defined and uniqueness…

An $R$-module $V$ over a semiring $R$ lacks zero sums (LZS) if $ x +y = 0 \; \Rightarrow \; x = y = 0$. More generally, asubmodule $W$ of $V$ is "summand absorbing", if $ \forall \, x, y \in V: \ x + y \in W \; \Rightarrow \; x \in W, \; y…

Let R be a commutative ring and S be an R-algebra. It is well-known that if N is an injective R-module, then Hom(S,N) is an injective S-module. The converse is not true, not even if R is a commutative noetherian local ring and S is its…

In this paper we study some frames associated to an $R$-module $M$. We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of $Max(M)$. We characterize the soberness of…

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 $\phi:\mathfrak{J}(R)\rightarrow\mathfrak{J}(R)\cup\{\emptyset\}$ be a reduction function of ideals of $R$ and let…