Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2 2 2015 02 01 ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES 83 96 EN M. Jafarpour Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. rmo4909@yahoo.com F. Alizadeh Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. falizadeh@yahoo.com 10.22044/jas.2015.358 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. Duplexes,semihypergroups,complementary feasible (semi)hypergroups http://jas.shahroodut.ac.ir/article_358.html http://jas.shahroodut.ac.ir/article_358_f99c12fe0b879e885797880dc7afd9b4.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2 2 2015 02 01 ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS 97 108 EN S. Alikhani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. alikhani@yazd.ac.ir S. Jahari Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. s.jahari@gmail.com 10.22044/jas.2015.359 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. Edge cover polynomial,edge covering,equivalence class,cubic graph,corona http://jas.shahroodut.ac.ir/article_359.html http://jas.shahroodut.ac.ir/article_359_03bd853b0f975a60d986af404d928abd.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2 2 2015 02 01 ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS 109 124 EN M. Habibi Department of Mathematics, University of Tafresh, P.O.Box 39518-79611, Tafresh, Iran. habibi.mohammad2@gmail.com 10.22044/jas.2015.360 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. Inverse skew power series extensions,Radical property,Semicommutative rings http://jas.shahroodut.ac.ir/article_360.html http://jas.shahroodut.ac.ir/article_360_3c473d1d286abc25947c292a6b305359.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2 2 2015 02 01 COHEN-MACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION 125 135 EN A. Esmaeelnezhad Faculty of Mathematical sciences and computer, University of Kharazmi, Tehran, Iran. esmaeilnejad@gmail.com 10.22044/jas.2015.361 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. Semi-dualizing ideal,Amalgamated duplication,Gorenstein homological dimension,Cohen-Macaulay homological dimension http://jas.shahroodut.ac.ir/article_361.html http://jas.shahroodut.ac.ir/article_361_50a50dd113314eebf1bad604ed0e91b0.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2 2 2015 02 01 COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS 137 146 EN Gh. Moghaddasi Department of Mathematics, Hakikm Sabzevari University, P.O.Bo 397, Sabzevar, Iran. r.moghadasi@hsu.ac.ir 10.22044/jas.2015.371 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. S-poset,cogenerator,regular injective,subdirectly irreducible http://jas.shahroodut.ac.ir/article_371.html http://jas.shahroodut.ac.ir/article_371_cf285a5a87885ed211e1f128762fbc2f.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2 2 2015 02 01 ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS 147 151 EN N. Ahanjideh Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran. ahanjidn@gmail.com H. Mousavi Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran. h.sadat68@yahoo.com 10.22044/jas.2015.372 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\$. non-commuting graph,\$K_4\$-free graph,\$K_{1,3}\$-free graph http://jas.shahroodut.ac.ir/article_372.html http://jas.shahroodut.ac.ir/article_372_7f1845805d519f0e1594759c85b7ed9d.pdf