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
M. Jafarpour
rmo4909@yahoo.com
1
F. Alizadeh
falizadeh@yahoo.com
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
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
S. Alikhani
alikhani@yazd.ac.ir
1
S. Jahari
s.jahari@gmail.com
2
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
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
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
M. Habibi
habibi.mohammad2@gmail.com
1
Department of Mathematics, University of Tafresh, P.O.Box 39518-79611, Tafresh, Iran.
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
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
A. Esmaeelnezhad
esmaeilnejad@gmail.com
1
Faculty of Mathematical sciences and computer, University of Kharazmi, Tehran, Iran.
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
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
Gh. Moghaddasi
r.moghadasi@hsu.ac.ir
1
Department of Mathematics, Hakikm Sabzevari University, P.O.Bo 397, Sabzevar, Iran.
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
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
N. Ahanjideh
ahanjidn@gmail.com
1
H. Mousavi
h.sadat68@yahoo.com
2
Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran.
Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran.
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