An ideal $I$ of a ring $R$ is called a right strongly Baer ideal if $r(I)=r(e)$, where $e$ is an idempotent, and there are right semicentral idempotents $e_{i}$ ($1\leq i\leq n$) with $ReR=Re_{1}R\cap Re_{2}R\cap...\cap ...

The notion of w−filters is introduced in an Almost Distributive Lattice(ADL) and properties are investigated. A necessary and sufficient condition is derived for a maximal filter of an ADL to become a w−filter which leads ...

The notion of hemicomplemented lattices is introduced and some of the properties of these algebras are studied. Some characterization theorems of hemicomplemented lattices are derived with the help of minimal prime D-filters, ...

‎Let $G=(V‎, ‎E)$ be a simple graph‎. ‎A set $C$ of vertices of $G$ is an identifying code of $G$ if for every two vertices $x$ and $y$ the sets $N_{G}[x] \cap C$ and $N_{G}[y] \cap C$ are non-empty and different‎. ‎Given ...

‎In this paper we continue our study of perpendicular graph of modules‎, ‎that was introduced in \cite{Hokkaido}‎. ‎Let $R$ be a ring and $M$ be an $R$-module‎. ‎Two modules $A$ and‎ ‎$B$ are called orthogonal‎, ‎written ...

In this paper, we introduce and study the concept of Jacobson monoform modules whichis a proper generalization of that of monoform modules. We present a characterization of semisimplerings in terms of Jacobson monoform ...

‎A *-ring‎ ‎$R$ is called a generalized $\pi$-Baer *-ring‎, ‎if for any projection invariant left ideal $Y$ of $R$‎, ‎the right annihilator of $Y^n$‎ ‎is generated‎, ‎as a right ideal‎, ‎by a projection, ‎for some positive ...

Let $S$ be a commutative pointed monoid. In this paper, some properties of admissible (Rees) short exact sequences of $S$-acts are investigated. In particular, it is shown that every admissible short exact sequence of ...

In this paper, we compute the common neighbourhood (abbreviated as CN) spectrum and the common neighbourhood energy of commuting conjugacy class graph of several families of finite non-abelian groups. As a consequence of ...

In this paper we extended the results of paper\linebreak ``On Closed Homotypical Varieties of Semigroups" and have shown that the homotypical varieties of semigroups defined by the identities  $axy=x^nayx$, $axy=xa^nya$[ ...

‎Let $R$ be an associative ring with identity‎. ‎In this paper we‎‎associate to every $R$-module $M$ a simple graph $\Gamma_e(M)$‎, which we call it the essentiality graph of $M$. The vertices of $\Gamma_e(M)$ are nonzero ...

A well-known enumerative problem is to count the number of ways a positive integer $n$ can be factorised as $n=n_1\times n_2\times\cdots\times n_{k}$, where $n_1\geqslant n_2 \geqslant \cdots \geqslant n_{k} >1$. In this ...

In this work, we introduce dual Rickart (Baer) modules via the con-cept of preradicals. It is shown that W is -d Rickart if and only ifW = (W) L such that (W) is a dual Rickart module. We provethat a module W is ...

The relationship between derivations and algebraic structures of quotient near-rings has become a fascinating topic in modern algebra in recent decades. Assume $\mathcal{N}$ is a near-ring and $P$ is its prime ideal. In ...

Let R be a commutative ring with unity. Let Nil(R) be the set of all nilpotent elements of R and Nil(R) = R \ Nil(R) be the set of all non-nilpotent elements of R. The non-nilpotent graph of R is a simple undirected graph ...

Given a matrix A with elements from a field of characteristic zero, the transin-verse A# of A is defined as the transpose of the matrix obtained by replacing the non-zero elements of A by their inverses and leaving zeros, ...

In this paper, we define the concept $I-$prime hyperideal in a multiplicative hyperring $R$. A proper hyperideal $P$ of $R$ is an $I-$prime hyperideal if for $a, b \in R$ with $ab \subseteq P-IP$ implies $a \in P$ or $b ...

Let $M$ and $N$ be bimodules over the unital $*$-rings $R$ and $B$, respectively.We investigate the notion of $R$-convexity and the corresponding notion of $R$-extreme points.We discuss the effect of an $f$-homomorphism ...

Let S be a commutative semiring with unity and U(S) be the set of all units of S. The unit graph of S, denoted by G(S), is the undirected graph with vertex set S and two distinct vertices x and y are adjacent if and only ...

Properties of prime filters and maximal filters of transitive GE-algebras are investigated. An element-wise characterization is derived for the smallest GE-filter containing a given set. It is proved that the set of all ...