@Article{Kazemi2014,
author="Kazemi, Ramin",
title="CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS",
journal="Algebraic Structures and Their Applications",
year="2014",
volume="1",
number="2",
pages="77-84",
abstract="The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of random variables on theK\^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this structure.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_493.html"
}
@Article{Alikhani2014,
author="Alikhani, Saeid
and Mirvakili, Saeed",
title="INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS",
journal="Algebraic Structures and Their Applications",
year="2014",
volume="1",
number="2",
pages="85-103",
abstract="Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ isindependent set of $G$, if no two vertices of $S$ are adjacent.The independence number $\alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $\Gamma(R)$ and ideal-based zero-divisor graph $\Gamma_I(R)$of a commutative ring $R$.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_494.html"
}
@Article{Azad2014,
author="Azad, Azizollah
and Elahinezhad, Nafiseh",
title="ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP",
journal="Algebraic Structures and Their Applications",
year="2014",
volume="1",
number="2",
pages="105-115",
abstract="Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is agraph $\Gamma_G$ as follows: Take $G\setminus Z(G)$ as vertices of$\Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yx\neq yx$. $\Gamma_G$ is called the non-commuting graph of $G$. In recent years many interesting works have been done in non-commutative graph of groups. Computing the clique number, chromatic number, Szeged index and Wiener index play important role in graph theory. In particular, the clique number of non-commuting graph of some the general linear groups has been determined. \nt Recently, Wiener and Szeged indiceshave been computed for $\Gamma_{PSL(2,q)}$, where $q\equiv 0 (mod~~4)$. In this paper we will compute the Szeged index for$\Gamma_{PSL(2,q)}$, where $q\not\equiv 0 (mod ~~ 4)$.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_495.html"
}
@Article{Khass2015,
author="Khass, Hossain
and Bazigaran, Behnam
and Ashrafi, Ali Reza",
title="A SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="1",
number="2",
pages="117-122",
abstract="In this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. It is proved that an abelian group of finite exponent is strongly coatomic.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_518.html"
}
@Article{Mahmoodi2015,
author="Mahmoodi, A.",
title="NILPOTENT GRAPHS OF MATRIX ALGEBRAS",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="1",
number="2",
pages="123-132",
abstract="Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $\Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = \{0\neq x \in R |\ xy \in N(R) \ for\ some\ y \in R^*\}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy \in N(R)$, or equivalently, $yx \in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left Artinian ring, then $\diam(\Gamma_{N}(R))\leqslant 3$. In this paper, using the concept of rank over commutative rings, we investigate basic properties of undirected nilpotent graph of matrix algebras. Moreover, some result on undirected nilpotent graph of matrix algebras over commutative rings are given. For instance, we prove that $\Gamma_{N}(M_{n}(R))$ is not planar for all $n\geqslant 2$. Furthermore, we show that $\diam(\Gamma_{N}(R))\leqslant \diam(\Gamma_{N}(M_{n}(R)))$ for an Artinian commutative ring $R$. Also, we prove that $\Gamma_{N}(M_{n}(R))\cong\Gamma_{N}(M_{n}(T(R)))$, where $T(R)$ be the total quotient ring of a commutative ring $R$",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_519.html"
}
@Article{Taghvaee2014,
author="Taghvaee, Fatemeh
and Fath-Tabar, Gholam Hossein",
title="SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM",
journal="Algebraic Structures and Their Applications",
year="2014",
volume="1",
number="2",
pages="133-141",
abstract="Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,\cdots,d_n)$, where $d_i$ is the degree of vertex $i$ and $A(G)$ the adjacency matrix of $G$. The signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of graph $G$ is defined as $T_k(G)=\sum_{i=1}^{n}q_i^{k}$, $k\geqslant 0$, where $q_1$,$q_2$, $\cdots$, $q_n$ are the eigenvalues of the signless Laplacian matrix of $G$. In this paper we first compute the $k-$th signless Laplacian spectral moments of a graph for small $k$ and then we order some graphs with respect to the signless Laplacian spectral moments.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_520.html"
}