##### 1. ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES

Volume 2, Issue 2 , Winter and Spring 2015, Pages 83-96

##### Abstract
In this paper using strongly duplexes we introduce a new class of (semi)hypergroups. The associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. Two computer programs written in MATLAB show that the two groups $Z_{2n}$ and $Z_{n}times Z_{2}$ produce a strongly duplex and ...  Read More

##### 2. ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS

S. Alikhani; S. Jahari

Volume 2, Issue 2 , Winter and Spring 2015, Pages 97-108

##### Abstract
Let $G$ be a simple graph of order $n$ and size $m$. The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$, where $e(G,i)$ is the number of edge coverings ...  Read More

##### 3. ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS

M. Habibi

Volume 2, Issue 2 , Winter and Spring 2015, Pages 109-124

##### Abstract
Let $alpha$ be an automorphism of a ring $R$. The authors [On skew inverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1) (2012) 138-156] applied the concept of Armendariz rings to inverse skew Laurent series rings and introduced skew inverse Laurent-serieswise Armendariz rings. In this article, ...  Read More

##### 4. COHEN-MACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION

Volume 2, Issue 2 , Winter and Spring 2015, Pages 125-135

##### Abstract
In this paper we use "ring changed'' Gorenstein homological dimensions to define Cohen-Macaulay injective, projective and flat dimensions. For doing this we use the amalgamated duplication of the base ring with semi-dualizing ideals. Among other results, we prove that finiteness of these new dimensions ...  Read More

##### 5. COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS

Volume 2, Issue 2 , Winter and Spring 2015, Pages 137-146

##### Abstract
In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets. Then we see that under some conditions, regular injectivity implies generator and cogenerator. Recalling Birkhoff's ...  Read More

##### 6. ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS

N. Ahanjideh; H. Mousavi

Volume 2, Issue 2 , Winter and Spring 2015, Pages 147-151

##### Abstract
Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ ...  Read More