ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES
Morteza
Jafarpour
Faculty of Mathematics, Vali-e-Asr University of Rafsanjan
author
Fatemeh
Alizadeh
faculty of Math
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
Saeid
Alikhani
Yazd University
author
Sommayeh
Jahari
Yazd University
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 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.
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
Mohammad
Habibi
Department of Mathematics, University of Tafresh
author
text
article
2015
eng
Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise 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.
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
Afsaneh
Esmaeelnezhad
Department of Mathematics, University of Kharazmi, Karaj, Iran
author
text
article
2015
eng
In this paper we use "ring changed'' Gorenstein homologicaldimensions to define Cohen-Macaulay injective, projective and flatdimensions. For doing this we use the amalgamated duplication of thebase 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
Gholamreza
Moghaddasi
Hakim Sabzevary university, Sabzevar, Iran
author
text
article
2015
eng
In this paper we study the notions of cogenerator and subdirectlyirreducible 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 injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theorem for the category ofordered right acts over an ordered monoid. Among other things, wegive the relations between cogenerators and subdirectlyirreducible 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
Neda
Ahanjideh
Shahrekord Univ.
author
Hajar
Mousavi
Shahrekord University
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