##### ON THE COMPUTATIONAL COMPLEXITY ASPECTS OF PERFECT ROMAN DOMINATION

Volume 10, Issue 2 , January 2023, Pages 189-202
##### Abstract
‎A perfect Roman dominating function (PRDF) on a graph $G$ is a function $f:V(G)\to \{0,1,2\}$ satisfying the condition that every vertex $u$ with $f(u) = 0$ is adjacent to exactly one vertex $v$ for which $f(v) = 2$‎. ‎The weight of a PRDF $f$ is the sum of the weights of the vertices under ...  Read More

##### r-CLEAN RINGS RELATIVE TO RIGHT IDEALS

H. Ibrahim Hakmi; B. Ali Alussein

Volume 10, Issue 2 , January 2023, Pages 203-224
##### Abstract
Abstract.An associative ring R with identity is called r¡clean ring if everyelement of R is the sum of a regular and an idempotent element. In this paper,we introduce the concept of r-clean rings relative to right ideal. We studyvarious properties of these rings. We give some relations between ...  Read More

I. Akray; Sh. Othman; A. Jabbar; H. Hussein

Volume 10, Issue 2 , January 2023, Pages 225-243
##### Abstract
Let $R= \bigoplus_{g \in G} R_g$ be a $G-$graded commutative ring with identity, $I$ be a graded ideal and let $M$ a $G-$graded unitary $R$-module, where $G$ is a semigroup with identity $e$. We introduce graded $I-$prime ideals (submodules) as a generalizations of the classical notions of prime ideals ...  Read More

##### FALTINGS’ LOCAL-GLOBAL PRINCIPLE FOR THE MINIMAXNESS OF LOCAL COHOMOLOGY MODULES DEFINED BY A SYSTEM OF IDEALS

Volume 10, Issue 2 , January 2023, Pages 245-258
##### Abstract
Let R be a commutative Noetherian ring with nonzero identity. Let φ be a system of ideals of R and let M, N two finitely generated R-modules. We prove that there are local- global principles for the finiteness and minimaxness of generalized local cohomology module H_φ^i (M, N) , in certain cases.  Read More

##### ON HOMOLOGICAL CLASSIFICATION OF MONOIDS BY CONDITION (PWPsc) OF RIGHT ACTS

Volume 10, Issue 2 , January 2023, Pages 259-283
##### Abstract
In this paper, we introduce Condition (PWPsc) as a generalization of Condition (PWP_E) of acts over monoids, and we observe that Condition (PWPsc) does not imply Condition (PWP_E). In general, we show that Condition (PWPsc) implies the property of being principally weakly flat, and that in left PSFmonoids, ...  Read More

##### INTUITIONISTIC FALLING SHADOWS APPLIED TO COMMUTATIVE IDEALS IN BCK-ALGEBRAS

R. A. Borzooei; X. L. Xin; Y. B. Jun

Volume 10, Issue 2 , January 2023, Pages 285-297
##### Abstract
The notion of commutative falling intuitionistic fuzzy ideal of a BCK-algebra is introduced and related properties are investigated. We verify that every commutative intuitionistic fuzzy ideal is a commutative falling intuitionistic fuzzy ideal, and provide example to show that a commutative falling ...  Read More

##### ON DETERMINING THE DISTANCE SPECTRUM OF A CLASS OF DISTANCE INTEGRAL GRAPHS

Seyed M. Mirafzal; R. Kogani

Volume 10, Issue 2 , January 2023, Pages 299-308
##### Abstract
The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix‎‎$D(G)$‎. ‎A graph is called distance integral if all of its‎‎distance eigenvalues are integers.‎‎Let $n$ and $k$ be integers with $n>2k‎, ‎k\geq1$‎. ‎The bipartite ...  Read More

##### ON THE PATH HYPEROPERATION AND ITS CONNECTIONS WITH HYPERGRAPH THEORY

R. Bayat Tajvar; M. Latifi

Volume 10, Issue 2 , January 2023, Pages 309-321
##### Abstract
In this paper, we introduce a path hyperoperation associated with a hypergraph,which is an extension of the Corsini’s hyperoperation.We investigate some related properties and study relations betweenthe path hyperoperation and hypergraph theory.  Read More

##### A NOTE ON Cc(X) VIA A TOPOLOGICAL RING

R. Mohamadian; M. Namdari; H. Najafian; S. Soltanpour

Volume 10, Issue 2 , January 2023, Pages 323-334
##### Abstract
Let $C_c(X)$ (resp., $C_c^*(X)$) denote the functionallycountable subalgebra of $C(X)$ (resp., $C^*(X)$),consisting of all functions (resp., bounded functions) with countable image.$C_c(X)$ (resp., $C_c^*(X)$) as a topological ring via $m_c$-topology (resp., $m^*_c$-topology) and $u_c$-topology (resp., ...  Read More

##### PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS

Volume 10, Issue 2 , January 2023, Pages 335-343
##### Abstract
‎Let $R$ be a commutative ring and $Z(R)$ be the set of its zero-divisors‎.‎The annihilator graph of $R$‎, ‎denoted by $AG(R)$ is a simple undirected graph whose vertex‎‎set is $Z(R)^*$‎, ‎the set of all nonzero zero-divisors of $R$‎, ‎and two distinct vertices ...  Read More

##### A GRAPH ASSOCIATED TO FILTERS OF A LATTICE

Sh. Ebrahimi Atani; M. Khoramdel; S. Dolati Pish Hesari; M. Nikmard Rostamalipour

Volume 10, Issue 2 , January 2023, Pages 345-359
##### Abstract
Let $L$ be a lattice with the least element $0$ and the greatest element $1$. In this paper, we associate a graph to filters of $L$, in which the vertex set is being the set of all non-trivial filters of $L$, and two distinct vertices $F$ and $E$ are adjacent if and only if $F \cap E \neq \{1\}$. We ...  Read More

##### WEAKLY BAER RINGS

S. Mehralinejadian; A. Moussavi; Sh. Sahebi

Volume 10, Issue 2 , January 2023, Pages 361-374
##### Abstract
We say a ring R with unity is left weakly Baer if the left annihilatorof any nonempty subset of R is right s-unital by right semicentral idempotents,which implies that R modulo the left annihilator of any nonempty subset isﬂat. It is shown that, unlike the Baer or right PP conditions, the weaklyBaer ...  Read More