Related papers: On graded weakly $J_{gr}$-semiprime submodules

It is known that graded cyclic modules over $S=K[x,y]$ have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over $S$. The purpose of this note is to study which conditions on $S$-modules ensure the WLP. We give an…

Let R be a commutative ring with unity and M be an R- module In this paper we introduce semi n- absorbing and (k, n)-closed submodules of modules over commutative rings, and investigate their basic properties.

In this article we introduce the notion of a controlled group graded ring. Let $G$ be a group, with identity element $e$, and let $R=\oplus_{g\in G} R_g$ be a unital $G$-graded ring. We say that $R$ is $G$-controlled if there is a…

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to defined the notion of quasi $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R and obtained some related results when M is a…

A subgroup $H$ of a finite group $G$ is submodular in $G$ if there is a subgroup chain $H=H_0\leq\ldots\leq H_i\leq H_{i+1}\leq \ldots \leq H_n=G$ such that $H_i$ is a modular subgroup of $H_{i+1}$ for every $i$. We investigate finite…

After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a \emph{weak lower $A$-semi-frame} and we study its properties. In…

The coprime commutators $\gamma_j^*$ and $\delta_j^*$ were recently introduced as a tool to study properties of finite groups that can be expressed in terms of commutators of elements of coprime orders. They are defined as follows. Let $G$…

In this paper R will denote a commutative ring with identity and M a nonzero unital R-module. We will generalize the concept of semiannihilator small submodules to the T-semiannihilator small submodules with respect to an arbitrary…

Let G be a finite group and {\sigma} = {{\sigma}_i, i \in I} be a partition of the set of all primes \mathbb{P}. A set \mathcal{H} of subgroups of G with 1 \in \mathcal{H} is said to be a complete Hall {\sigma}-set of G if every…

The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are…

Let $S$ be a semiring. An $S$-semimodule $M$ is called a multiplication semimodule if for each subsemimodule $N$ of $M$ there exists an ideal $I$ of $S$ such that $N=IM$. In this paper we investigate some properties of multiplication…

The goal of this note is to classify the weakly closed unipotent subgroups in the split Chevalley groups. In an application we show under some mild assumptions on the characteristic that the Lie algebra of a connected simple algebraic group…

The aim of this paper is to propose an extension of the Wilf conjecture to semimodules over a numerical semigroup through a new approach toward the solution of the Wilf conjecture on numerical semigroups. The key point is the introduction…

Let $R$ be a commutative Noetherian ring, $\fa$ be an ideal of $R$ and $M$ be an $R$-module. The main purpose of this paper is to answer the Hartshorn's questions in the class of weakly Laskerian modules. It is shown that if $s\geq 1$ is a…

Let R be a commutative ring with identity. A prime submodule P of an R-module M is called coprimely structured if, whenever P is coprime to each element of an arbitrary family of submodules of M, the intersection of the family is not…

Let $R=\mathbb K[x,y,z]$ be a standard graded polynomial ring where $\mathbb K$ is an algebraically closed field of characteristic zero. Let $M = \oplus_j M_j$ be a finite length graded $R$-module. We say that $M$ has the Weak Lefschetz…

The weakly zero-divisor graph $W\Gamma(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$ and two distinct vertices $x$, $y$ are adjacent if and only if there exist $w\in {\rm…

Representation theory of Lie (super)algebras has attracted significant research interest for many years, especially due to its applications in theoretical physics; in this regard, the representation theory of affine Lie (super)algebras is…

We introduce and study the so-called {\it weakly $\sqrt{J}U$ rings} (hereafter abbreviated as {\it $W\sqrt{J}U$ rings} for short), in which every unit is of the form $j+1$ or $j-1$ for some $j$ in $\sqrt{J(R)} : = \{x \in R : x^n \in J(R)…

Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be weakly S-embedded in $G$ if there exists $K\unlhd G$ such that $HK$ is S-quasinormal in $G$ and $H\cap K\leq H_{seG}$, where $H_{seG}$ is the subgroup generated by all those…