It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we recall a generalization of ...

Let $G=(V, E)$ be a graph. A set $S subseteq V$ is called a dominating set of $G$ if for every $vin V-S$ there is at least one vertex $u in N(v)$ such that $uin S$. The domination number of $G$, denoted by $gamma(G)$, is ...

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$ -module. Let $S(M)$ be the set of all submodules of $M$ and $phi :S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function. A proper submodule $N$ of ...

In this article we consider the $m$-topology on linebreak $M(X,mathscr{A})$, the ring of all real measurable functions on a measurable space $(X, mathscr{A})$, and we denote it by $M_m(X,mathscr{A})$. We show that ...

In this paper, the notion of fuzzy medial filters of a pseudo BE-algebra is defined, and some of the properties are investigated. We show that the set of all fuzzy medial filters of a pseudo BE-algebra is a complete lattice. ...

A subset of the vertex set of a graph $G$ is called a zero forcing set if by considering them colored and, as far as possible, a colored vertex with exactly one non-colored neighbor forces its non-colored neighbor to get ...

Let $L$ be a finite dimensional Lie algebra. A subalgebra $H$ of $L$ is called a $c^{#}$-ideal of $L$, if there is an ideal $K$ of $L$ with $L=H+K$ and $Hcap K$ is a $CAP$-subalgebra of $L$. This is analogous to the concept ...

The infinite family of groups defined by the presentation $G_p=langle x, y|x^p=y^p,; xyx^my^n=1rangle$, in which $p$ is a prime in ${2,3,5}$ and $m,ninmathbb{N}_0$, will be considered and finite and infinite groups in the ...

In this paper we consider some properties of derivations of lattices and show that (i) for a derivation $d$ of a lattice $L$ with the maximum element $1$, it is monotone if and only if $d(x) le d(1)$ for all $xin L$ (ii) ...

‎Let $R$ be a commutative ring and $M$ be an $R$-module‎. ‎The‎ ‎annihilator graph of $M$‎, ‎denoted by $AG(M)$ is a simple undirected‎ ‎graph associated to $M$ whose the set of vertices is‎ ‎$Z_R(M) setminus {rm Ann}_R(M)$ ...