2015
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2
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ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES
2
2
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 its associated hypergroup is a complementary feasible hypergroup.
1

83
96


Morteza
Jafarpour
Faculty of Mathematics, ValieAsr University of Rafsanjan
Faculty of Mathematics, ValieAsr University
Iran
rmo4909@yahoo.com


Fatemeh
Alizadeh
faculty of Math
faculty of Math
Iran
falizadeh@yahoo.com
Duplexes
semihypergroups
complementary feasible (semi)hypergroups
ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS
2
2
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 of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we study theedge cover polynomials of cubic graphs of order $10$.We show that all cubic graphs of order $10$ (especially the Petersen graph) aredetermined uniquely by their edge cover polynomials.
1

97
108


Saeid
Alikhani
Yazd University
Yazd University
Iran
alikhani@yazd.ac.ir


Sommayeh
Jahari
Yazd University
Yazd University
Iran
s.jahari@gmail.com
Edge cover polynomial
edge covering
equivalence class
cubic graph
corona
ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS
2
2
Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurentserieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurentserieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse skew power series type. We determine the radicals of theinverse skew Laurent series ring $R((x^{1};alpha))$, in terms ofthose of $R$. We also prove that several properties transfer between$R$ and the inverse skew Laurent series extension$R((x^{1};alpha))$, in case $R$ is a strongly Armendariz ring ofinverse skew power series type.
1

109
124


Mohammad
Habibi
Department of Mathematics, University of Tafresh
Department of Mathematics, University of
Iran
habibi.mohammad2@gmail.com
Inverse skew power series extensions
Radical property
Semicommutative rings
COHENMACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION
2
2
In this paper we use "ring changed'' Gorenstein homologicaldimensions to define CohenMacaulay injective, projective and flatdimensions. For doing this we use the amalgamated duplication of thebase ring with semidualizing ideals. Among other results, we prove that finiteness of these new dimensions characterizes CohenMacaulay rings with dualizing ideals.
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125
135


Afsaneh
Esmaeelnezhad
Department of Mathematics, University of Kharazmi, Karaj, Iran
Department of Mathematics, University of
Iran
esmaeilnejad@gmail.com
Semidualizing ideal
Amalgamated duplication
Gorenstein homological dimension
CohenMacaulay homological dimension
COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF SPOSETS
2
2
In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of Sposet. First we give somenecessary and sufficient conditions for a cogenerator $S$posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible Sposets and give this theorem for the category ofordered right acts over an ordered monoid. Among other things, wegive the relations between cogenerators and subdirectlyirreducible Sposets.
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137
146


Gholamreza
Moghaddasi
Hakim Sabzevary university, Sabzevar, Iran
Hakim Sabzevary university, Sabzevar, Iran
Iran
r.moghadasi@hsu.ac.ir
Sposet
cogenerator
regular injective
subdirectly irreducible
ON THE GROUPS WITH THE PARTICULAR NONCOMMUTING GRAPHS
2
2
Let $G$ be a nonabelian 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 $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.
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147
151


Neda
Ahanjideh
Shahrekord Univ.
Shahrekord Univ.
Iran
ahanjidn@gmail.com


Hajar
Mousavi
Shahrekord University
Shahrekord University
Iran
h.sadat68@yahoo.com
noncommuting graph
$K_4$free graph
$K_{1
3}$free graph