Shahrood University of TechnologyJournal of Algebraic Systems2345-51282220150201ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES839635810.22044/jas.2015.358ENMorteza JafarpourFaculty of Mathematics, Vali-e-Asr University of RafsanjanFatemeh Alizadehfaculty of MathJournal Article20131121In 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.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282220150201ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS9710835910.22044/jas.2015.359ENSaeid AlikhaniYazd UniversitySommayeh JahariYazd UniversityJournal Article20140430Let $G$ be a simple graph of order $n$ and size $m$.<br />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.<br /> The edge cover polynomial of $G$ is the polynomial<br />$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,<br />where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and<br />$rho(G)$ is the edge covering number of $G$. In this paper we study the<br />edge cover polynomials of cubic graphs of order $10$.<br />We show that all cubic graphs of order $10$ (especially the Petersen graph) are<br />determined uniquely by their edge cover polynomials.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282220150201ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS10912436010.22044/jas.2015.360ENMohammad HabibiDepartment of Mathematics, University of TafreshJournal Article20140521Let $alpha$ be an automorphism of a ring $R$. The authors [On skew<br />inverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)<br />(2012) 138-156] applied the concept of Armendariz rings to inverse<br />skew Laurent series rings and introduced skew inverse<br />Laurent-serieswise Armendariz rings. In this article, we study on a<br />special type of these rings and introduce strongly Armendariz rings<br />of inverse skew power series type. We determine the radicals of the<br />inverse skew Laurent series ring $R((x^{-1};alpha))$, in terms of<br />those of $R$. We also prove that several properties transfer between<br />$R$ and the inverse skew Laurent series extension<br />$R((x^{-1};alpha))$, in case $R$ is a strongly Armendariz ring of<br />inverse skew power series type.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282220150201COHEN-MACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION12513536110.22044/jas.2015.361ENAfsaneh EsmaeelnezhadDepartment of Mathematics, University of Kharazmi, Karaj, IranJournal Article20140724In this paper we use "ring changed'' Gorenstein homological<br />dimensions to define Cohen-Macaulay injective, projective and flat<br />dimensions. For doing this we use the amalgamated duplication of the<br />base ring with semi-dualizing ideals. Among other results, we prove that finiteness of these new dimensions characterizes Cohen-Macaulay rings with dualizing ideals.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282220150201COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS13714637110.22044/jas.2015.371ENGholamreza MoghaddasiHakim Sabzevary university, Sabzevar, IranJournal Article20140220In this paper we study the notions of cogenerator and subdirectly<br />irreducible in the category of S-poset. First we give some<br />necessary and sufficient conditions for a cogenerator $S$-posets.<br />Then we see that under some conditions, regular injectivity<br />implies generator and cogenerator. Recalling Birkhoff's<br />Representation Theorem for algebra, we study subdirectly<br />irreducible S-posets and give this theorem for the category of<br />ordered right acts over an ordered monoid. Among other things, we<br />give the relations between cogenerators and subdirectly<br />irreducible S-posets.Shahrood University of TechnologyJournal of Algebraic Systems2345-51282220150201ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS14715137210.22044/jas.2015.372ENNeda AhanjidehShahrekord Univ.Hajar MousaviShahrekord UniversityJournal Article20150127Let $G$ 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 $K_{1,3<br />}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.