Yazd UniversityAlgebraic Structures and Their Applications2382-97616220191101On perfectness of dot product graph of a commutative ring17139910.22034/as.2019.1399ENNaziAbachiDepartment of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 14168-94351, IranShervinSahebiDepartment of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 14168-94351, IranJournal Article20181225Let $A$ be a commutative ring with nonzero identity, and $1\leq n<\infty$ be an integer, and <br />$R=A\times A\times\cdots\times A$ ($n$ times). The total dot product graph of $R$ is the (undirected) graph $TD(R)$ with vertices $R^*=R\setminus \{(0,0,\dots,0)\}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $x\cdot y=0\in A$ (where $x\cdot y$ denote the normal dot product of $x$ and $y$). <br /> Let $Z(R)$ denote the set of all zero-divisors of $R$. Then the zero-divisor dot product graph of $R$ is the induced subgraph $ZD(R)$ of $TD(R)$ with vertices $Z(R)^*=Z(R)\setminus \{(0,0,\dots,0)\}$. It follows that if $\Gamma(A)$ is not perfect, then $ZD(R)$ (and hence $TD(R)$) is not perfect.<br />In this paper we investigate perfectness of the graphs $TD(R)$ and $ZD(R)$.https://as.yazd.ac.ir/article_1399_cc6ff88a41313de7665ac17156e473df.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101Groups whose set of vanishing elements is exactly a conjugacy class912142610.22034/as.2019.1426ENSajjad MahmoodRobatiDepartment of mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.0000-0002-9076-2513Journal Article20190204Let $G$ be a finite group. We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $\chi$ of $G$ such that $\chi(g)=0$. In this paper, we classify groups whose set of vanishing elements is exactly a conjugacy class.https://as.yazd.ac.ir/article_1426_443d31130e9d11d0a053f38be7fda313.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101H$^*$-condition on the set of submodules of a module1320142710.22034/as.2019.1427ENAli RezaMoniri HamzekolaeeDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar0000-0002-2852-7870Journal Article20190408In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand<br />$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,<br />a homomorphic image of a $H^*$ duo module satisfies $H^*$.https://as.yazd.ac.ir/article_1427_994a6c2c0b2bd9f31607c92131216852.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101The automorphism group of the reduced complete-empty $X-$join of graphs2138142810.22034/as.2019.1428ENAdelTadayyonfarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran0000-0002-1157-9682Ali RezaAshrafiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran0000-0002-2858-0663Journal Article20171231Suppose $X$ is a simple graph. The $X-$join $\Gamma$ of a set of<br />complete or empty graphs $\{X_x \}_{x \in V(X)}$ is a simple graph with the following vertex and edge sets:<br />\begin{eqnarray*}<br />V(\Gamma) &=& \{(x,y) \ | \ x \in V(X) \ \& \ y \in<br />V(X_x) \},\\ E(\Gamma) &=& \{<br />(x,y)(x^\prime,y^\prime) \ | \ xx^\prime \in E(X) \ or \ else \<br />x = x^\prime \ \& \ yy^\prime \in E(X_x)\}.<br />\end{eqnarray*}<br />The $X-$join graph $\Gamma$ is said to be reduced if $x, y \in V(X)$, $x \ne y$ and $N_X(x) \setminus \{ y\} = N_X(y) \setminus \{ x\}$ imply that $(i)$ if $xy \not\in E(X)$ then the graphs $X_x$ or $X_y$ are non-empty; $(ii)$ if $xy \in E(X)$ then $X_x$ or $X_y$ are not complete graphs. The aim of this paper is to explore how the graph theoretical properties of $X-$join of graphs effect on its automorphism group. Among other results we compute the automorphism group of reduced complete-empty $X-$join of graphs.https://as.yazd.ac.ir/article_1428_d2e9fce60d59a5965c18062f0026dec2.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101On the eigenvalues of Cayley graphs on generalized dihedral groups3945148110.22034/as.2019.1481ENFatemehAfshariDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.MohammadMaghasediDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranJournal Article20180723Let $\Gamma$ be a graph with adjacency eigenvalues $\lambda_1\leq\lambda_2\leq\ldots\leq\lambda_n$. Then the energy of $\Gamma$, a concept defined in 1978 by Gutman, is defined as $\mathcal{E}(G)=\sum_{i=1}^n|\lambda_i|$. Also the Estrada index of $\Gamma$, which is defined in 2000 by Ernesto Estrada, is defined as $EE(\Gamma)=\sum_{i=1}^ne^{\lambda_i}$.<br />In this paper, we compute the eigenvalues, energy and Estrada index of Cayley graphs on generalized dihedral groups. As an application, we compute these items for honeycomb toroidal graphs and Cayley graphs on dihedral groups.https://as.yazd.ac.ir/article_1481_b5a0215e25300daa27f8357e69329412.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976162201911012-absorbing $I$-prime and 2-absorbing $I$-second submodules4755148210.22034/as.2019.1482ENFaranakFarshadifarDepartment of Mathematics, Farhangian University, Tehran, Iran0000-0001-7600-994XJournal Article20180501Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.https://as.yazd.ac.ir/article_1482_f244bd463c9e275f3a71143c735b5c44.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101Some finite groups with divisibility graph containing no triangles5765148310.22034/as.2019.1483ENDanialKhoshnevisSchool of Mathematics, Iran University of science and Technology, Tehran, IranZohrehMostaghimSchool of Mathematics, Iran University of Science and Technology, Tehran, Iran.0000-0002-9724-0515Journal Article20190525Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $\sigma^{\ast}(G)=2$, a finite simple group $G$ that satisfies the one-prime power hypothesis, a group of type($A$),($B$) or ($C$) and certain metacyclic $p-$groups and a minimal non-metacyclic $p-$group where $p$ is a prime number. We will show that the divisibility graph $D(G)$ for all of them has no triangles.https://as.yazd.ac.ir/article_1483_87b8563e10d4c7d9435c7e4a2b2b0f02.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101Some remarks on generalizations of classical prime submodules6780148510.22034/as.2019.1485ENMasoudZolfaghariDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.Mohammad HoseinMoslemi KoopaeiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.0000-0003-2671-8515Journal Article20180423Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $\phi:S(M)\rightarrow S(M)\cup \lbrace\emptyset\rbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$\phi$-classical prime submodule, if whenever $r_{1},\ldots,r_{n-1}\in R$ and $m\in M$ with $r_{1}\ldots r_{n-1}m\in N\setminus\phi(N)$, then $r_{1}\ldots r_{i-1}r_{i+1}\ldots r_{n-1}m\in N$, for some $i\in\lbrace 1,\ldots, n-1\rbrace$ $(n\geqslant 3)$.<br />In this work, $(n-1, n)$-$\phi$-classical prime submodules are studied and some results are established.https://as.yazd.ac.ir/article_1485_0e20932e679114025d09ee6dffa7ca10.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101The existence totally reflexive covers8186148610.22034/as.2019.1486ENZahraHeidarianDepartment of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh,
Iran.0000-0001-8788-0407Journal Article20180811Let $R$ be a commutative Noetherian ring. We prove that over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover<br />$\varphi:C \rightarrow M$ such that $C$ is finitely generated and the projective dimension of $\Ker\varphi$ is finite and $\varphi$ is surjective.https://as.yazd.ac.ir/article_1486_b92b829ea109a8df9db22610a0de01e2.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101Local cohomology modules and Cousin complexes87100160710.22034/as.2019.1607ENAlirezaVahidiDepartment of Mathematics, Payame Noor University (PNU), P.O.BOX, 19395-4697, Tehran, Iran0000-0003-2967-6832FaisalHassaniDepartment of Mathematics, Payame Noor University (PNU), P.O.BOX, 19395-4697, Tehran, IranMaryamSenshenasDepartment of Mathematics, Payame Noor University (PNU), P.O.BOX, 19395-4697, Tehran, IranJournal Article20190307Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $X$ an arbitrary $R$--module, $\mathcal{F}$ a filtration of $\operatorname{Spec}(R)$ which admits $X$, and $s, s', t, t'$ non-negative integers such that $s+ t= s'+ t'$. In this paper, we study the membership of $R$--modules $\operatorname{H}^{s}_\mathfrak{a}(\operatorname{H}^{t- 1}(\operatorname{C}_R(\mathcal{F}, X)))$ and $\operatorname{H}^{s'- 1}(\operatorname{H}^{t'}_\mathfrak{a}(\operatorname{C}_R(\mathcal{F}, X)))$ in Serre subcategories of the category of $R$--modules and find some sufficient conditions which ensure the existence of an isomorphism between them, where $\operatorname{C}_R(\mathcal{F},X)$ is the Cousin complex for $X$ with respect to $\mathcal{F}$. As applications, we give some new facts and represent some older facts about the local cohomology modules and the Cousin complexes.https://as.yazd.ac.ir/article_1607_a5546eb62089ac16d99183ff50e25834.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101Regular and strongly soft $\Gamma$- relations on fuzzy soft $\Gamma$-hyperrings101113161010.22034/as.2019.1610ENSohrabOstadhadi DehkordiDepartment of mathematics, University of Hormozgan, Hormozgan, Bandar abbas, Iran.0000-0003-2323-550XBehnazSheikh HoseiniDepartment of Mathematics, Shahid Beheshti University, Tehran IranJournal Article20180427The concept of fuzzy soft $\Gamma$-hyperrings introduced by J. Zhan et al. as a generalization of the soft rings. In this paper, we prove the equivalence relation $\mu^{\ast}$ defined by J. Zhan et al. is a strongly soft $\Gamma$-regular relation and hyperoperations defined on quotient fuzzy soft $\Gamma$-hyperrings are just operations. Also, we define the equivalence relation $\mu^{\ast}_I$ as a generalization the relation $\mu^{\ast}$ and consider quotient fuzzy soft $\Gamma$-hyperrings and isomorphism theorems by this<br />regular relation.https://as.yazd.ac.ir/article_1610_aea4eb7bdf991921415d3604167d4463.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97616220191101A characterization of some simple unitary groups via order and degree pattern of solvable graph115127161410.22034/as.2019.1614ENBanafshehAkbariDepartment of Mathematics, Sahand University of Technology, Tabriz, IRAN.Journal Article20190320The solvable graph associated with a finite group $G$, denoted by ${\Gamma}_{\rm s}(G)$, is a simple graph whose vertices are the prime divisors of $|G|$ and two distinct primes $p$ and $q$ are joined by an edge if and only if there exists a solvable subgroup of $G$ whose order is divisible by $pq$. In this paper, we give a<br />characterization for projective special unitary groups $U_3(q)$ with some certain conditions by the solvable graph.https://as.yazd.ac.ir/article_1614_606d24656435f8966698b0621f65782e.pdf