Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
2
2017
01
01
FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES
85
95
EN
M.
Rezaei
Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.
mehdrezaei@gmail.com
Z.
Foruzanfar
Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.
zforouzanfar@gmail.com
10.22044/jas.2017.850
Let $G$ be a finite group and $Z(G)$ be the center of $G$. For a subset $A$ of $G$, we define $k_G(A)$, the number of conjugacy classes of $G$ which intersect $A$ non-trivially. In this paper, we verify the structure of all finite groups $G$ which satisfy the property $k_G(G-Z(G))=5$ and classify them.
Finite group,Frobenius group,Conjugacy class
http://jas.shahroodut.ac.ir/article_850.html
http://jas.shahroodut.ac.ir/article_850_f26adfb749347531a3cb078626440a73.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
2
2017
01
01
FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS
97
101
EN
F.
Forouzesh
Faculty of Mathematics and Computing, Higher Education Complex of Bam, Ker-
man, Iran
ffrouzesh@yahoo.com
10.22044/jas.2017.851
Abstract. In this paper, we introduce the notion of fuzzy obstinate ideals in MV -algebras. Some properties of fuzzy obstinate ideals are given. Not only we give some characterizations of fuzzy obstinate ideals, but also bring the extension theorem of fuzzy obstinate ideal of an MV -algebra A. We investigate the relationships between fuzzy obstinate ideals and the other fuzzy ideals of an MV -algebra. We describe the transfer principle for fuzzy obstinate ideals in terms of level subsets. In addition, we show that if mu is a fuzzy obstinate ideal of A such that mu(0)in [0; 1/2], then A/mu is a Boolean algebra. Finally, we define the notion of a normal fuzzy obstinate ideal and investigate some properties.
MV-algebra,fuzzy normal,fuzzy obstinate,fuzzy Boolean
http://jas.shahroodut.ac.ir/article_851.html
http://jas.shahroodut.ac.ir/article_851_08ccea2270f1cc3558fbf666ad8998c9.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
2
2017
01
01
RADICAL OF FILTERS IN RESIDUATED LATTICES
111
121
EN
S.
Motamed
Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.
somayeh.motamed@iauba.ac.ir
10.22044/jas.2017.852
In this paper, the notion of the radical of a filter in residuated lattices is defined and several characterizations of the radical of a filter are given. We show that if F is a positive implicative filter (or obstinate filter), then Rad(F)=F. We proved the extension theorem for radical of filters in residuated lattices. Also, we study the radical of filters in linearly ordered residuated lattices.
(Maximal) Prime filter,Radical,Residuated lattice
http://jas.shahroodut.ac.ir/article_852.html
http://jas.shahroodut.ac.ir/article_852_9a18ec2a81ec3a16def3083c7ce891e7.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
2
2017
01
01
REES SHORT EXACT SEQUENCES OF S-POSETS
123
134
EN
R.
Khosravi
Department of Mathematics, Fasa University, P.O.Box 74617-81189, Fasa, Iran.
khosravi@fasau.ac.ir
10.22044/jas.2017.853
In this paper the notion of Rees short exact sequence for S-posets is introduced, and we investigate the conditions for which these sequences are left or right split. Unlike the case for S-acts, being right split does not imply left split. Furthermore, we present equivalent conditions of a right S-poset P for the functor Hom(P;-) to be exact.
S-posets,pomonoids,Rees short exact sequence,projective
http://jas.shahroodut.ac.ir/article_853.html
http://jas.shahroodut.ac.ir/article_853_51ae2012410695a2524b1b1489d9be5d.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
2
2017
01
01
MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
135
153
EN
A.
Alhevaz
Department of Mathematics, Shahrood University of Technology, P.O. Box: 316-
3619995161, Shahrood, Iran.
a.alhevaz@gmail.com
M.
Baghipur
Department of Mathematics, Shahrood University of Technology, P.O. Box: 316-
3619995161, Shahrood, Iran.
maryamb8989@gmail.com
10.22044/jas.2017.854
Let $G=(V(G),E(G))$ be a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. The (first) edge-hyper Wiener index of the graph $G$ is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where $d_{e}(f,g|G)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $E(G)$ and $d_{e}(f|G)=sum_{gin E(G)}d_{e}(f,g|G)$. In this paper we use a method, which applies group theory to graph theory, to improving mathematically computation of the (first) edge-hyper Wiener index in certain graphs. We give also upper and lower bounds for the (first) edge-hyper Wiener index of a graph in terms of its size and Gutman index. Also we investigate products of two or more graphs and compute the second edge-hyper Wiener index of the some classes of graphs. Our aim in last section is to find a relation between the third edge-hyper Wiener index of a general graph and the hyper Wiener index of its line graph. of two or more graphs and compute edge-hyper Wiener number of some classes of graphs.
Edge-hyper Wiener index,line graph,Gutman index,connectivity,edge-transitive graph
http://jas.shahroodut.ac.ir/article_854.html
http://jas.shahroodut.ac.ir/article_854_2486403d0b8da2a0bb248f7cd1fcd96b.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
4
2
2017
01
01
THE ZERO-DIVISOR GRAPH OF A MODULE
155
171
EN
A.
Naghipour
Department of Mathematics, Shahrekord University, P.O. Box 115, Shahrekord,
Iran.
naghipourar@yahoo.com
10.22044/jas.2017.858
Let $R$ be a commutative ring with identity and $M$ an $R$-module. In this paper, we associate a graph to $M$, say ${Gamma}({}_{R}M)$, such that when $M=R$, ${Gamma}({}_{R}M)$ coincide with the zero-divisor graph of $R$. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for ${Gamma}({}_{R}M)$. We show that ${Gamma}({}_{R}M)$ is connected with ${diam}({Gamma}({}_{R}M))leq 3$ and if ${Gamma}({}_{R}M)$ contains a cycle, then $gr({Gamma}({}_{R}M))leq 4$. We also show that ${Gamma}({}_{R}M)=emptyset$ if and only if $M$ is a prime module. Among other results, it is shown that for a reduced module $M$ satisfying DCC on cyclic submodules, $gr{Gamma}({}_{R}M)=infty$ if and only if ${Gamma}({}_{R}M)$ is a star graph. Finally, we study the zero-divisor graph of free $R$-modules.
Annilhilator,diameter,girth,reduced module,zero-divisor graph
http://jas.shahroodut.ac.ir/article_858.html
http://jas.shahroodut.ac.ir/article_858_dc9a03e1918e0e0bd28530d1103281ff.pdf