In this paper, we define a 2-absorbing $delta$-primary element and a weakly 2-absorbing $delta$-primary element in a compactly generated multiplicative lattice $L$. We obtain some properties of these elements. We give a ...

For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where ...

Let $M$ be a module over a commutative ring $R$, $Z_{*}(M)$ be its set of weak zero-divisor elements, andif $min M$, then let $I_m=(Rm:_R M)={rin R : rMsubseteq Rm}$. The annihilator graph of $M$ is the (undirected) ...

Let  $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. We say that $I$ satisfies the persistence property if  $mathrm{Ass}_R(R/I^k)subseteq mathrm{Ass}_R(R/I^{k+1})$ for all positive integers $kgeq 1$, which ...

First, we apply the method presented by Zahra Sepasdar in the two-dimensional case to construct a basis of a three dimensional cyclic code. We then generalize this construction to a general $s$-dimensional cyclic code.

An associative ring R, not necessarily commutative and not necessarily with identity, is called Boolean-zero square orBZS if every element of R is either idempotent or nilpotent of index 2. We continue our investigation ...

Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial ...

The question of identifying the elements of the center of a nearring and of determining when that center is a subnearring is an area of continued research.  We consider the centers of centralizer nearrings, $M_I(S_n)$, ...

For every inverse semigroup $S$ with subsemigroup $E$ of idempotents, necessary and sufficient conditions are obtained for the semigroup algebra $l ^{1}(S)$  to be $hat{phi}$-amenable and $hat{phi}$-module amenable. Also, ...

Providing a description of linked ideals in a commutative Noetherian ring in terms of some associated prime ideals, we make a characterization of Cohen-Macaulay, Gorenstein and regular local rings in terms of their linked ...

In this paper, we introduce a class of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a$ of a ring $R$ is called {it weakly $J$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or ...

Let $R$ be a commutative ring with identity and $M$ be an $R$-module. The main purpose of this paper is to introduce and investigate the notion of classical and strongly classical $n$-absorbing second submodules as a dual ...

Let $M$ be a lattice module over a  $C$-lattice $L$.  Let $Spec^{p}(M)$ be the collection of all prime elements of $M$. In this article, we consider a  topology on $Spec^{p}(M)$, called the classical Zariski topology and ...

In this paper, we define the co-intersection graph $G(A)$ of an \(S\)-act \(A\) which is a graph whose vertices are non-trivial subacts of \(A\) and two  distinct  vertices \(B_1\) and \( B_2\) are adjacent if \(B_1 \cup ...

The comaximal intersection graph $CI(R)$ of ideals of a ring $R$ is an undirected graph whose vertex set is the collection of all non-trivial (left) ideals of $R$ and any two vertices $I$ and  $J$ are adjacent if and only ...

In the preprint of ``Pseudo-Gorenstein and Level Hibi Rings,'' Ene, Herzog, Hibi, and Saeedi Madani assert (Theorem 4.3) that for a regular planar lattice $L$ with poset of join-irreducibles $P$, the following are ...

In this paper, we discussed a method to construct a global sheaf space using graphs via Maximal compatibility blocks (MCB's) and we proposed the correspondence between graphs and sheaves. Further we discussed the sheaf ...

‎In this paper‎, ‎we introduce a new algorithm for constructing a‎ ‎symmetric pentadiagonal matrix by using three interlacing spectrum‎, ‎say $(\lambda_i)_{i=1}^n$‎, ‎$(\mu_i)_{i=1}^n$ and $(\nu_i)_{i=1}^n$‎ ‎such ...

A graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which ...

Let $R$ be a commutative ring with non-zero identity, and $\delta :\mathcal{I(R)}\rightarrow\mathcal{I(R)}$ be an ideal expansion where $\mathcal{I(R)}$ is the set of all ideals of $R$. In this paper, we introduce the ...