Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES
175
192
EN
H.
Hejazipour
Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord,
Iran.
h.hejazipour@iran.ir
A.
R.
Naghipour
0000-0002-7178-6173
Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, City,
Country.
naghipourar@yahoo.com
10.22044/jas.2020.9745.1474
Let $M(X, \mathcal{A}, \mu)$ be the ring of real-valued measurable functions<br />on a measurable space $(X, \mathcal{A})$ with measure $\mu$.<br />In this paper, we study the zero-divisor graph of $M(X, \mathcal{A}, \mu)$,<br />denoted by $\Gamma(M(X, \mathcal{A}, \mu))$.<br />We give the relationships among graph properties of $\Gamma(M(X, \mathcal{A}, \mu))$, ring properties of<br />$M(X, \mathcal{A}, \mu)$ and measure properties of $(X, \mathcal{A}, \mu)$.<br />Finally, we investigate the continuity properties of $\Gamma(M(X, \mathcal{A}, \mu))$.
Rings of measurable functions,Measure space,zero-divisor graph,Continuous function
https://jas.shahroodut.ac.ir/article_2191.html
https://jas.shahroodut.ac.ir/article_2191_21a43a34fff3e583e0985cad32831aa1.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
DISTANCE LAPLACIAN SPECTRUM OF THE COMMUTING GRAPH OF FINITE CA-GROUPS
193
201
EN
M.
Torktaz
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O. Box 87317–53153, Kashan, I. R. Iran.
me.torktaz@gmail.com
A. R.
Ashrafi
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O. Box 87317–53153, Kashan, I. R. Iran.
ashrafi@kashanu.ac.ir
10.22044/jas.2020.9214.1452
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.
Distance matrix,commuting graph,distance Laplacian spectrum
https://jas.shahroodut.ac.ir/article_2192.html
https://jas.shahroodut.ac.ir/article_2192_82158eda796ef5fb134f98973cc4c965.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
ANNIHILATING-IDEAL GRAPH OF C(X)
203
217
EN
M.
Badie
Department of Mathematics, Jundi-Shapur University of Technology, P.O. Box
64615/334, Dezful, Iran.
badie@jsu.ac.ir
10.22044/jas.2021.10008.1496
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 and only if AG(X) is not triangulated. Radius, girth, dominating number and clique number of the AG(X) are investigated. It is proved that c(X) <= dt(AG(X)) ,= w(X) and wAG(X) = χAG(X) = c(X).
Rings of real-valued continuous functions,Annihilating-ideal graph,Clique number,Chromatic number,Cellularity
https://jas.shahroodut.ac.ir/article_2193.html
https://jas.shahroodut.ac.ir/article_2193_db1062600571017f02164e5aab615fcb.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
TOPICS ON CONTINUOUS INVERSE ALGEBRAS
219
227
EN
A.
Naziri-Kordkandi
0000-0001-5962-4035
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.
ali_naziri@pnu.ac.ir
10.22044/jas.2021.9747.1475
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.<br /><br />
Keywords: continuous inverse algebra,topological zero divisor,spectrum,multiplicative linear map
https://jas.shahroodut.ac.ir/article_2194.html
https://jas.shahroodut.ac.ir/article_2194_a53f31b8c2bd1f972570a19168a8d36d.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
(7,K) GIRTH-8 QC-LDPC CODES WITH AN EXPLICIT CONSTRUCTION
229
239
EN
M.
Majdzadeh
Department of Mathematics, Shahrekord University, Shahrekord, Iran.
marjanmajdzade@gmail.com
M.
Gholami
0000-0002-3174-0138
Department of Mathematics, Shahrekord University, Shahrekord, Iran.
gholami-m@sci.sku.ac.ir
Gh.
Raeisi
Department of Mathematics, Shahrekord University, Shahrekord, Iran.
ghaffar.raisy@gmail.com
10.22044/jas.2021.8911.1434
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 been considered small as possible. In this paper, for $J=7$, a class of $(7,K)$ QC-LDPC codes with girth 8 is generated by an explicit method such that the lower-bounds of the constructed codes remarkably are better than the state-of-the-art bound $(K-1)(K^2+K)+1$.
QC-LDPC codes,explicit constructions,girth,exponent matrix
https://jas.shahroodut.ac.ir/article_2195.html
https://jas.shahroodut.ac.ir/article_2195_c0df1d88cfdf2c920bfa4dcd2111e302.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
Geometric Hypergroups
241
257
EN
M.
Al Tahan
Department of Mathematics, Lebanese International University, Bekaa, Lebanon.
madeline.tahan@liu.edu.lb
B.
Davvaz
https://orcid.org/00
Department of Mathematics, Yazd University, Yazd, Iran.
davvaz@yazd.ac.ir
10.22044/jas.2021.9981.1493
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 using generalized Cayley graphs over hypergroups. Then we study a large scale of geometry with respect to the structure of hypergroups and we prove that metric spaces of finitely generated hypergroups coming from different generating sets are quasi-isometric.
Cayley graph,hypergroup,geometric hypergroup
https://jas.shahroodut.ac.ir/article_2196.html
https://jas.shahroodut.ac.ir/article_2196_429071f73af8f14407a78631514f916a.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
SOME INEQUALITIES FOR POLYNILPOTENT MULTIPLIER OF POWERFULL p-GROUPS
259
265
EN
M.
Alizadeh Sanati
Department of Mathematics, University of Golestan, P.O. Box ,155 Gorgan, Iran.
m.alizadeh@gu.ac.ir
10.22044/jas.2021.9465.1462
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 of Mashakekhy and Maohammadzadeh’s in 2007 to polynilpotent multipliers.
powerful p-groups,polynilpotent multiplier of groups,exponent,minimum number of generators of a group
https://jas.shahroodut.ac.ir/article_2197.html
https://jas.shahroodut.ac.ir/article_2197_d26668847ad433a45fe3e0bbf37199bb.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
ON SOME TOTAL GRAPHS ON FINITE RINGS
267
280
EN
M.
Taghidoust Laskukalayeh
0000_0003_1330_6327
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Guilan, P.O. Box 19141, Rasht, Iran.
m.taghidoust.lk@gmail.com
M.
Gholamnia Taleshani
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of
Guilan, P.O. Box 19141, Rasht, Iran.
m.gholamniai@gmail.com
A.
Abbasi
Department of Pure Mathematics, Faculty of Mathematical Sciences, University
of Guilan, P.O. Box 19141, Rasht, Iran.Guilan, Rasht, Iran.
aabbasi@guilan.ac.ir
10.22044/jas.2021.10004.1495
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))<br />where p is a prime and m and n are positive integers and investigate some graph theoretical properties with some of its fundamental subgraphs.
Total graph,Decomposition,Graphs on commutative rings
https://jas.shahroodut.ac.ir/article_2198.html
https://jas.shahroodut.ac.ir/article_2198_c13bc973c806d636f9e791201321a3da.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS
281
298
EN
Seyed M. A.
Khatami
Department of Computer Science, Birjand University of Technology, Birjand, Iran.
khatami@birjandut.ac.ir
10.22044/jas.2021.10296.1509
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 $a \leftrightarrow b=(a\too b)*(b\too a)$. We will show that when the continuous scale $[0,1]$ is endowed to be a BL-algebra, then this topology admits some of the most important properties of the metric topology. Finally, we will show that this topology can be examined by a similar topology on dual of BL-algebras as well.
BL-algebra,dual of BL-algebra,topological BL-algebra
https://jas.shahroodut.ac.ir/article_2199.html
https://jas.shahroodut.ac.ir/article_2199_dfd241457e2e2e2e3a972fe61649d936.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
ON DERIVATIONS OF PSEUDO-BL ALGEBRA
299
322
EN
S.
Rahnama
Department of Mathematics, Yazd University, P.O. Box 8915818411, Yazd, Iran.
somayeh.rahnama@stu.yazd.ac.ir
Seid M.
Anvariyeh
https://orcid.org/00
Department of Mathematics, Yazd University, P.O. Box 8915818411, Yazd, Iran.
anvariyeh@yazd.ac.ir
S.
Mirvakili
Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697
Tehran, Iran.
saeed_mirvakili@pnu.ac.ir
B.
Davvaz
https://orcid.org/00
Department of Mathematics, Yazd University, P.O. Box 8915818411, Yazd, Iran.
davvaz@yazd.ac.ir
10.22044/jas.2021.10532.1519
Pseudo-BL algebras are a natural generalization of BL-algebras and of pseudo-MV algebras.<br />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 $(\varphi , \psi)$-derivations are defined on these types. Finally, several related properties are discussed.
BL-algebra,derivation,Pseudo-BL algebras
https://jas.shahroodut.ac.ir/article_2200.html
https://jas.shahroodut.ac.ir/article_2200_aab84573f268dc999086748782c7d729.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
FINITENESS PROPERTIES OF FORMAL LOCAL COHOMOLOGY MODULES
323
333
EN
Sh.
Rezaei
Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
3697, Tehran, Iran.
sha.rezaei@gmail.com
A.
Riahini Komachali
Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
3697, Tehran, Iran.
reyahini1367@gmail.com
10.22044/jas.2021.9875.1484
In this paper, we investigate some properties of top formal local<br />cohomology FdimM=aM<br />a (M). Among other things, we determine AttR(FdimM=aM<br />a (M)),<br />in the case that FdimM=aM<br />a (M) is an artinian module. Also we show that FdimM=aM<br />a (M)<br />is artinian if and only if it is minimax..
formal local cohomology,Local cohomology,artinianness
https://jas.shahroodut.ac.ir/article_2201.html
https://jas.shahroodut.ac.ir/article_2201_327925adab9d8fb376af5551e12dcc7f.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
9
2
2022
01
01
ON THE m_c-TOPOLOGY ON THE FUNCTIONALLY COUNTABLE SUBALGEBRA OF C(X)
335
345
EN
A.
Veisi
Faculty of Petroleum and Gas, Yasouj University, Gachsaran, Iran.
veisi75@gmail.com
10.22044/jas.2021.10325.1510
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 space, then $C_c(X)$ is first countable if and only if $C(X)$ with the $m$-topology is first countable. Also, the set of all zero-divisors of $C_c(X)$ is closed if and only if $X$ is an almost $P$-space. We show that if $X$ is a strongly zero-dimensional space and $U$ is the set of all units of $C_c(X)$, then the maximal ring of quotients of $C_c(U)$ and $C_c(C_c(X))$ are isomorphic.
Functionally countable subalgebra,m_c-topology,pseudocompact space,zero-dimensional space
https://jas.shahroodut.ac.ir/article_2202.html
https://jas.shahroodut.ac.ir/article_2202_9f86a0f31960713951c05e51499ce3df.pdf