1. ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES

H. Hejazipour; A. R. Naghipour

Volume 9, Issue 2 , Winter and Spring 2022, Pages 175-192

http://dx.doi.org/10.22044/jas.2020.9745.1474

Abstract
  Let $M(X, \mathcal{A}, \mu)$ be the ring of real-valued measurable functionson a measurable space $(X, \mathcal{A})$ with measure $\mu$.In this paper, we study the zero-divisor graph of $M(X, \mathcal{A}, \mu)$,denoted by $\Gamma(M(X, \mathcal{A}, \mu))$.We give the relationships among graph properties ...  Read More

2. DISTANCE LAPLACIAN SPECTRUM OF THE COMMUTING GRAPH OF FINITE CA-GROUPS

M. Torktaz; A. R. Ashrafi

Volume 9, Issue 2 , Winter and Spring 2022, Pages 193-201

http://dx.doi.org/10.22044/jas.2020.9214.1452

Abstract
  The commuting graph of a finite group $G$, $\mathcal{C}(G)$, is a simple graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $xy = yx$. The aim of this paper is to compute the distance Laplacian spectrum and the distance Laplacian energy of the commuting graph of $CA$-groups.  Read More

3. ANNIHILATING-IDEAL GRAPH OF C(X)

M. Badie

Volume 9, Issue 2 , Winter and Spring 2022, Pages 203-217

http://dx.doi.org/10.22044/jas.2021.10008.1496

Abstract
  In this article the annihilating-ideal graph of the ring C(X) is studied. We have tried to associate the graph properties of AG(X), the ring properties of C(X) and the topological properties of X. It is shown that X has an isolated point if and only if R is a direct summand of C(X) and this happens if ...  Read More

4. TOPICS ON CONTINUOUS INVERSE ALGEBRAS

A. Naziri-Kordkandi

Volume 9, Issue 2 , Winter and Spring 2022, Pages 219-227

http://dx.doi.org/10.22044/jas.2021.9747.1475

Abstract
  In this paper, we first provide some counterexamples and derive some new results concerning the usual and singular spec- trum of an element in continuous inverse algebras. Then we continue our investigation about the characterizations of multiplicative linear maps and their related results in these algebras.  Read More

5. (7,K) GIRTH-8 QC-LDPC CODES WITH AN EXPLICIT CONSTRUCTION

M. Majdzadeh; M. Gholami; Gh. Raeisi

Volume 9, Issue 2 , Winter and Spring 2022, Pages 229-239

http://dx.doi.org/10.22044/jas.2021.8911.1434

Abstract
  Recently, for each row weight $K$ and column-weight $J$, $3\le J< K$, several classes of $(J,K)$ quasi-cyclic (QC) low-density parity-check (LDPC) codes with girth 8 have been constructed explicitly such that their corresponding lower-bounds on the size of circulant permutation matrices (CPMs) have ...  Read More

6. Geometric Hypergroups

M. Al Tahan; B. Davvaz

Volume 9, Issue 2 , Winter and Spring 2022, Pages 241-257

http://dx.doi.org/10.22044/jas.2021.9981.1493

Abstract
  The aim of this paper is to extend the notion of geometric groups to geometric hypergroups and to investigate the interaction between algebraic and geometric properties of hypergroups. In this regard, we first define a metric structure on hypergroups via word metric and present some examples on it by ...  Read More

7. SOME INEQUALITIES FOR POLYNILPOTENT MULTIPLIER OF POWERFULL p-GROUPS

M. Alizadeh Sanati

Volume 9, Issue 2 , Winter and Spring 2022, Pages 259-265

http://dx.doi.org/10.22044/jas.2021.9465.1462

Abstract
  In this paper we present some inequalities for the order, the exponent, and the number of generators of the polynilpotent multiplier, the Baer invariant with respect to the variety of polynilpotent groups of class row (c_1; · · · ; c_t) of a powerful p-group.Our results extend some ...  Read More

8. ON SOME TOTAL GRAPHS ON FINITE RINGS

M. Taghidoust Laskukalayeh; M. Gholamnia Taleshani; A. Abbasi

Volume 9, Issue 2 , Winter and Spring 2022, Pages 267-280

http://dx.doi.org/10.22044/jas.2021.10004.1495

Abstract
  We give a decomposition of total graphs on some finite commutative rings R = Zm, where the set of zero-divisors of R is not an ideal. In particular, we study the total graph T(􀀀(Z2npm))where p is a prime and m and n are positive integers and investigate some graph theoretical properties with some ...  Read More

9. A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS

Seyed M. A. Khatami

Volume 9, Issue 2 , Winter and Spring 2022, Pages 281-298

http://dx.doi.org/10.22044/jas.2021.10296.1509

Abstract
  This paper is devoted to introduce a topology on BL-algebras, makes them semitopological algebras. For any BL-algebra $\mathcal{L}=(L, \wedge, \vee, *, \too , 0, 1)$, the introduced topology is defined by a distance-like function between elements of $L$ which is defined by $a \leftrightarrow b=(a\too ...  Read More

10. ON DERIVATIONS OF PSEUDO-BL ALGEBRA

S. Rahnama; Seid M. Anvariyeh; S. Mirvakili; B. Davvaz

Volume 9, Issue 2 , Winter and Spring 2022, Pages 299-322

http://dx.doi.org/10.22044/jas.2021.10532.1519

Abstract
  Pseudo-BL algebras are a natural generalization of BL-algebras and of pseudo-MV algebras.In this paper the notions of five different types of derivations on a \pbl\ as generalizations of derivations of a BL-algebra are introduced. Moreover, as an extension of derivations of a \pbl , the notions of $(\varphi ...  Read More

11. FINITENESS PROPERTIES OF FORMAL LOCAL COHOMOLOGY MODULES

Sh. Rezaei; A. Riahini Komachali

Volume 9, Issue 2 , Winter and Spring 2022, Pages 323-333

http://dx.doi.org/10.22044/jas.2021.9875.1484

Abstract
  In this paper, we investigate some properties of top formal localcohomology FdimM=aMa (M). Among other things, we determine AttR(FdimM=aMa (M)),in the case that FdimM=aMa (M) is an artinian module. Also we show that FdimM=aMa (M)is artinian if and only if it is minimax..  Read More

12. ON THE m_c-TOPOLOGY ON THE FUNCTIONALLY COUNTABLE SUBALGEBRA OF C(X)

A. Veisi

Volume 9, Issue 2 , Winter and Spring 2022, Pages 335-345

http://dx.doi.org/10.22044/jas.2021.10325.1510

Abstract
  In this paper, we consider the $m_c$-topology on $C_c(X)$, the functionally countable subalgebra of $C(X)$. We show that a Tychonoff space $X$ is countably pseudocompact if and only if the $m_c$-topology and the $u_c$-topology on $C_c(X)$ coincide. It is shown that whenever $X$ is a zero-dimensional ...  Read More