Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2 2 2015 02 01 ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES 83 96 358 10.22044/jas.2015.358 EN M. Jafarpour Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. F. Alizadeh Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. Journal Article 2013 11 21 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. http://jas.shahroodut.ac.ir/article_358_f99c12fe0b879e885797880dc7afd9b4.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2 2 2015 02 01 ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS 97 108 359 10.22044/jas.2015.359 EN S. Alikhani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. S. Jahari Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. Journal Article 2014 04 30 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<br />\$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<br />\$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. http://jas.shahroodut.ac.ir/article_359_03bd853b0f975a60d986af404d928abd.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2 2 2015 02 01 ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS 109 124 360 10.22044/jas.2015.360 EN M. Habibi Department of Mathematics, University of Tafresh, P.O.Box 39518-79611, Tafresh, Iran. Journal Article 2014 05 21 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 a<br />special 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. http://jas.shahroodut.ac.ir/article_360_3c473d1d286abc25947c292a6b305359.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2 2 2015 02 01 COHEN-MACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION 125 135 361 10.22044/jas.2015.361 EN A. Esmaeelnezhad Faculty of Mathematical sciences and computer, University of Kharazmi, Tehran, Iran. Journal Article 2014 07 24 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. http://jas.shahroodut.ac.ir/article_361_50a50dd113314eebf1bad604ed0e91b0.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2 2 2015 02 01 COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS 137 146 371 10.22044/jas.2015.371 EN Gh. Moghaddasi Department of Mathematics, Hakikm Sabzevari University, P.O.Bo 397, Sabzevar, Iran. Journal Article 2014 02 20 In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-poset. First we give some<br />necessary 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. http://jas.shahroodut.ac.ir/article_371_cf285a5a87885ed211e1f128762fbc2f.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2 2 2015 02 01 ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS 147 151 372 10.22044/jas.2015.372 EN N. Ahanjideh Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran. H. Mousavi Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran. Journal Article 2015 01 27 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\$. http://jas.shahroodut.ac.ir/article_372_7f1845805d519f0e1594759c85b7ed9d.pdf