eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-02-01
2
2
83
96
10.22044/jas.2015.358
358
ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES
Morteza Jafarpour
rmo4909@yahoo.com
1
Fatemeh Alizadeh
falizadeh@yahoo.com
2
Faculty of Mathematics, Vali-e-Asr University of Rafsanjan
faculty of Math
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
Duplexes
semihypergroups
complementary feasible (semi)hypergroups
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-02-01
2
2
97
108
10.22044/jas.2015.359
359
ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS
Saeid Alikhani
alikhani@yazd.ac.ir
1
Sommayeh Jahari
s.jahari@gmail.com
2
Yazd University
Yazd University
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.
http://jas.shahroodut.ac.ir/article_359_03bd853b0f975a60d986af404d928abd.pdf
Edge cover polynomial
edge covering
equivalence class
cubic graph
corona
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-02-01
2
2
109
124
10.22044/jas.2015.360
360
ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS
Mohammad Habibi
habibi.mohammad2@gmail.com
1
Department of Mathematics, University of Tafresh
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.
http://jas.shahroodut.ac.ir/article_360_3c473d1d286abc25947c292a6b305359.pdf
Inverse skew power series extensions
Radical property
Semicommutative rings
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-02-01
2
2
125
135
10.22044/jas.2015.361
361
COHEN-MACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION
Afsaneh Esmaeelnezhad
esmaeilnejad@gmail.com
1
Department of Mathematics, University of Kharazmi, Karaj, Iran
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.
http://jas.shahroodut.ac.ir/article_361_50a50dd113314eebf1bad604ed0e91b0.pdf
Semi-dualizing ideal
Amalgamated duplication
Gorenstein homological
dimension
Cohen-Macaulay homological dimension
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-02-01
2
2
137
146
10.22044/jas.2015.371
371
COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS
Gholamreza Moghaddasi
r.moghadasi@hsu.ac.ir
1
Hakim Sabzevary university, Sabzevar, Iran
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.
http://jas.shahroodut.ac.ir/article_371_cf285a5a87885ed211e1f128762fbc2f.pdf
S-poset
cogenerator
regular injective
subdirectly irreducible
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2015-02-01
2
2
147
151
10.22044/jas.2015.372
372
ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS
Neda Ahanjideh
ahanjidn@gmail.com
1
Hajar Mousavi
h.sadat68@yahoo.com
2
Shahrekord Univ.
Shahrekord University
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
non-commuting graph
$K_4$-free graph
$K_{1
3}$-free graph