Shahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES175192219110.22044/jas.2020.9745.1474ENH. HejazipourDepartment of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord,
Iran.A. R.NaghipourDepartment of Mathematical Sciences, Shahrekord University, P.O. Box 115, City,
Country.0000-0002-7178-6173Journal Article20200529Let $M(X, \mathcal{A}, \mu)$ 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 $\Gamma(M(X, \mathcal{A}, \mu))$.https://jas.shahroodut.ac.ir/article_2191_21a43a34fff3e583e0985cad32831aa1.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101DISTANCE LAPLACIAN SPECTRUM OF THE COMMUTING GRAPH OF FINITE CA-GROUPS193201219210.22044/jas.2020.9214.1452ENM. TorktazDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O. Box 87317–53153, Kashan, I. R. Iran.A. R. AshrafiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Kashan, P.O. Box 87317–53153, Kashan, I. R. Iran.Journal Article20200111The 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.https://jas.shahroodut.ac.ir/article_2192_82158eda796ef5fb134f98973cc4c965.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101ANNIHILATING-IDEAL GRAPH OF C(X)203217219310.22044/jas.2021.10008.1496ENM. BadieDepartment of Mathematics, Jundi-Shapur University of Technology, P.O. Box
64615/334, Dezful, Iran.Journal Article20200824In 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).https://jas.shahroodut.ac.ir/article_2193_db1062600571017f02164e5aab615fcb.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101TOPICS ON CONTINUOUS INVERSE ALGEBRAS219227219410.22044/jas.2021.9747.1475ENA. Naziri-KordkandiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran,
Iran.0000-0001-5962-4035Journal Article20200530In 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 />https://jas.shahroodut.ac.ir/article_2194_a53f31b8c2bd1f972570a19168a8d36d.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101(7,K) GIRTH-8 QC-LDPC CODES WITH AN EXPLICIT CONSTRUCTION229239219510.22044/jas.2021.8911.1434ENM. MajdzadehDepartment of Mathematics, Shahrekord University, Shahrekord, Iran.M. GholamiDepartment of Mathematics, Shahrekord University, Shahrekord, Iran.0000-0002-3174-0138Gh. RaeisiDepartment of Mathematics, Shahrekord University, Shahrekord, Iran.Journal Article20190916Recently, 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 $(K-1)(K^2+K)+1$.https://jas.shahroodut.ac.ir/article_2195_c0df1d88cfdf2c920bfa4dcd2111e302.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101Geometric Hypergroups241257219610.22044/jas.2021.9981.1493ENM. Al TahanDepartment of Mathematics, Lebanese International University, Bekaa, Lebanon.B. DavvazDepartment of Mathematics, Yazd University, Yazd, Iran.https://orcid.org/00Journal Article20200815The 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.https://jas.shahroodut.ac.ir/article_2196_429071f73af8f14407a78631514f916a.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101SOME INEQUALITIES FOR POLYNILPOTENT MULTIPLIER OF POWERFULL p-GROUPS259265219710.22044/jas.2021.9465.1462ENM. Alizadeh SanatiDepartment of Mathematics, University of Golestan, P.O. Box ,155 Gorgan, Iran.Journal Article20200314In 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.https://jas.shahroodut.ac.ir/article_2197_d26668847ad433a45fe3e0bbf37199bb.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101ON SOME TOTAL GRAPHS ON FINITE RINGS267280219810.22044/jas.2021.10004.1495ENM. Taghidoust LaskukalayehDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Guilan, P.O. Box 19141, Rasht, Iran.0000_0003_1330_6327M. Gholamnia TaleshaniDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of
Guilan, P.O. Box 19141, Rasht, Iran.A. AbbasiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University
of Guilan, P.O. Box 19141, Rasht, Iran.Guilan, Rasht, Iran.Center of Excellence for Mathematical Modeling, Optimization and Combinatorial
Computing (MMOCC), University of Guilan, Rasht, Iran.Journal Article20200822We 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.https://jas.shahroodut.ac.ir/article_2198_c13bc973c806d636f9e791201321a3da.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS281298219910.22044/jas.2021.10296.1509ENSeyed M. A. KhatamiDepartment of Computer Science, Birjand University of Technology, Birjand, Iran.Journal Article20201122This 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.https://jas.shahroodut.ac.ir/article_2199_dfd241457e2e2e2e3a972fe61649d936.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101ON DERIVATIONS OF PSEUDO-BL ALGEBRA299322220010.22044/jas.2021.10532.1519ENS. RahnamaDepartment of Mathematics, Yazd University, P.O. Box 8915818411, Yazd, Iran.Seid M. AnvariyehDepartment of Mathematics, Yazd University, P.O. Box 8915818411, Yazd, Iran.0000-0001-7535-1698S. MirvakiliDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697
Tehran, Iran.B. DavvazDepartment of Mathematics, Yazd University, P.O. Box 8915818411, Yazd, Iran.https://orcid.org/00Journal Article20210204Pseudo-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.https://jas.shahroodut.ac.ir/article_2200_aab84573f268dc999086748782c7d729.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101FINITENESS PROPERTIES OF FORMAL LOCAL COHOMOLOGY MODULES323333220110.22044/jas.2021.9875.1484ENSh. RezaeiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
3697, Tehran, Iran.A. Riahini KomachaliDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-
3697, Tehran, Iran.Journal Article20200708In 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..https://jas.shahroodut.ac.ir/article_2201_327925adab9d8fb376af5551e12dcc7f.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101ON THE m_c-TOPOLOGY ON THE FUNCTIONALLY COUNTABLE SUBALGEBRA OF C(X)335345220210.22044/jas.2021.10325.1510ENA. VeisiFaculty of Petroleum and Gas, Yasouj University, Gachsaran, Iran.Journal Article20201202In 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.https://jas.shahroodut.ac.ir/article_2202_9f86a0f31960713951c05e51499ce3df.pdf