##### A SURVEY ON THE FUSIBLE PROPERTY OF SKEW PBW EXTENSIONS

S. Higuera; A. Reyes

Volume 10, Issue 1 , September 2022, Pages 1-29
##### Abstract
We present several results that establish the fusible and the regular left fusible properties of the family of noncommutative rings known as skew Poincar'e-Birkhoff-Witt extensions. Our treatment is based on the recent works of Ghashghaei and McGovern [13], and Kosan and Matczuk [31] concerning the left ...  Read More

##### VOLUNTARY GE-FILTERS AND FURTHER RESULTS OF GE-FILTERS IN GE-ALGEBRAS

A. Borumand Saeid; A. Rezaei; R. Bandaru; Y. B. Jun

Volume 10, Issue 1 , September 2022, Pages 31-47
##### Abstract
Further properties on (belligerent) GE-filters are discussed, and the quotient GEalgebra via a GE-filter is established. Conditions for the set →c to be a belligerent GE-filterare provided. The extension property of belligerent GE-filter is composed. The notions of abalanced element, a balanced ...  Read More

##### VALUED-POTENT (GENERAL) MULTIRINGS

M. Hamidi; A. A. Tavakoli; R. Ameri

Volume 10, Issue 1 , September 2022, Pages 49-68
##### Abstract
Abstract. This paper extends multirings to a novel concept as general multirings, investigates their properties and presents a special general multirings as notation of (m; n)-potent general multirings. This study analyzes the di fferences between class of multirings, general multirings and general hyperrings ...  Read More

##### A NOTE ON RELATIVE GENERALIZED COHEN-MACAULAY MODULES

A. Ghanbari Doust

Volume 10, Issue 1 , September 2022, Pages 69-78
##### Abstract
Let a be a proper ideal of a ring R. A finitely generated R-module M is said to be a-relative generalized Cohen-Macaulay if f_a (M)=cd(a ,M). In this note, we introduce a suitable notion of length of a module to characterize the above mentioned modules. Also certain syzygy modules over a relative Cohen-Macaulay ...  Read More

##### H-SETS AND APPLICATIONS ON Hv-GROUPS

Volume 10, Issue 1 , September 2022, Pages 79-93
##### Abstract
In this paper, the notion of H-sets on Hv-groups is introduced and some related properties are investigated and some examples are given. In this regards, the concept of regular, strongly regular relations and homomorphism of H-sets are adopted. Also, the classical isomorphism theorems of groups are generalized ...  Read More

##### GRADED SEMIPRIME SUBMODULES OVER NON-COMMUTATIVE GRADED RINGS

P. Ghiasvand; F. Farzalipour

Volume 10, Issue 1 , September 2022, Pages 95-110
##### Abstract
Let $G$ be a group with identity $e$, $R$ be an associative graded ring and $M$ be a $G$-graded $R$-module. In this article, we intruduce the concept of graded semiprimesubmodules over non-commutative graded rings. First, we study graded prime $R$-modulesover non-commutative graded rings and we get some ...  Read More

##### DIVISOR TOPOLOGIES AND THEIR ENUMERATION

F. Esmaeeli; K. Mirzavaziri; M. Mirzavaziri

Volume 10, Issue 1 , September 2022, Pages 111-119
##### Abstract
‎For a positive integer $m$‎, ‎a subset of divisors of $m$ is called a \textit{divisor topology on $m$} if it contains $1$ and $m$ and it is closed under taking $\gcd$ and $\rm lcm$‎. ‎If $m=p_1\dots p_n$ is a square free positive integer‎, ‎then a divisor topology $m$ corresponds ...  Read More

##### NORMAL INJECTIVE RESOLUTION OF GENERAL KRASNER HYPERMODULES

M. Hamidi; F. Faraji; R. Ameri; Kh. Ahmadi-amoli

Volume 10, Issue 1 , September 2022, Pages 121-145
##### Abstract
In this paper, we construct the concept of general  Krasner  hyperring based on the  ring  structures and the left general Krasner hypermodule based on the  module structures.  This study introduces  the  trivial left general Krasner hypermodules and  proves ...  Read More

##### SUMS OF UNITS IN SOME CLASSES OF NEAT RINGS

N. Pouyan

Volume 10, Issue 1 , September 2022, Pages 147-153
##### Abstract
A ring R is said to be clean if every element of R is a sumof an idempotent and a unit. A ring R is a neat ring if every nontrivialhomomorphic image is clean. In this paper, first, it is proved that everyelement of some classes of neat rings is n-tuplet-good if no factor ringof such rings isomorphic ...  Read More

##### THE IDENTIFYING CODE NUMBER AND FUNCTIGRAPHS

A. Shaminejad; E. Vatandoost

Volume 10, Issue 1 , September 2022, Pages 155-166
##### Abstract
Let G = (V (G); E(G)) be a simple graph. A set D of vertices G is an identifying code of G; if for every two vertices x and y the sets N_G[x] \ D and N_G[y] \ D are non- empty and different. The minimum cardinality of an identifying code in graph G is the identifying code number of G and it is denoted ...  Read More

##### JORDAN HIGHER DERIVATIONS, A NEW APPROACH

Sayed. Kh. Ekrami

Volume 10, Issue 1 , September 2022, Pages 167-177