ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES M. Jafarpour Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. author F. Alizadeh Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. author text article 2015 eng 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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 2 v. 2 no. 2015 83 96 http://jas.shahroodut.ac.ir/article_358_f99c12fe0b879e885797880dc7afd9b4.pdf dx.doi.org/10.22044/jas.2015.358 ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS S. Alikhani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. author S. Jahari Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. author text article 2015 eng 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 the edge cover polynomials of cubic graphs of order \$10\$. We show that all cubic graphs of order \$10\$ (especially the Petersen graph) are determined uniquely by their edge cover polynomials. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 2 v. 2 no. 2015 97 108 http://jas.shahroodut.ac.ir/article_359_03bd853b0f975a60d986af404d928abd.pdf dx.doi.org/10.22044/jas.2015.359 ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS M. Habibi Department of Mathematics, University of Tafresh, P.O.Box 39518-79611, Tafresh, Iran. author text article 2015 eng 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, we study on aspecial type of these rings and introduce strongly Armendariz rings of inverse skew power series type. We determine the radicals of the inverse skew Laurent series ring \$R((x^{-1};alpha))\$, in terms of those 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 of inverse skew power series type. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 2 v. 2 no. 2015 109 124 http://jas.shahroodut.ac.ir/article_360_3c473d1d286abc25947c292a6b305359.pdf dx.doi.org/10.22044/jas.2015.360 COHEN-MACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION A. Esmaeelnezhad Faculty of Mathematical sciences and computer, University of Kharazmi, Tehran, Iran. author text article 2015 eng 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 characterizes Cohen-Macaulay rings with dualizing ideals. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 2 v. 2 no. 2015 125 135 http://jas.shahroodut.ac.ir/article_361_50a50dd113314eebf1bad604ed0e91b0.pdf dx.doi.org/10.22044/jas.2015.361 COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS Gh. Moghaddasi Department of Mathematics, Hakikm Sabzevari University, P.O.Bo 397, Sabzevar, Iran. author text article 2015 eng 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 Representation Theorem for algebra, we study subdirectly irreducible S-posets and give this theorem for the category of ordered right acts over an ordered monoid. Among other things, we give the relations between cogenerators and subdirectly irreducible S-posets. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 2 v. 2 no. 2015 137 146 http://jas.shahroodut.ac.ir/article_371_cf285a5a87885ed211e1f128762fbc2f.pdf dx.doi.org/10.22044/jas.2015.371 ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS N. Ahanjideh Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran. author H. Mousavi Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran. author text article 2015 eng 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\$ or \$Q_8\$. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 2 v. 2 no. 2015 147 151 http://jas.shahroodut.ac.ir/article_372_7f1845805d519f0e1594759c85b7ed9d.pdf dx.doi.org/10.22044/jas.2015.372