2017
4
2
0
0
FINITE GROUPS WITH FIVE NONCENTRAL CONJUGACY CLASSES
2
2
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 $A$ nontrivially. In this paper, we verify the structure of all finite groups $G$ which satisfy the property $k_G(GZ(G))=5$ and classify them.
1

85
95


M.
Rezaei
Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.
Department of Mathematics, Buein Zahra Technical
Iran
mehdrezaei@gmail.com


Z.
Foruzanfar
Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.
Buein Zahra Technical University, Buein Zahra,
Iran
zforouzanfar@gmail.com
Finite group
Frobenius group
Conjugacy class
FUZZY OBSTINATE IDEALS IN MVALGEBRAS
2
2
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.
1

97
101


F.
Forouzesh
Faculty of Mathematics and Computing, Higher Education Complex of Bam, Ker
man, Iran
Faculty of Mathematics and Computing, Higher
Iran
ffrouzesh@yahoo.com
MValgebra
fuzzy normal
fuzzy obstinate
fuzzy Boolean
RADICAL OF FILTERS IN RESIDUATED LATTICES
2
2
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.
1

111
121


S.
Motamed
Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.
Department of Mathematics, Bandar Abbas Branch,
Iran
somayeh.motamed@iauba.ac.ir
(Maximal) Prime filter
Radical
Residuated lattice
REES SHORT EXACT SEQUENCES OF SPOSETS
2
2
In this paper the notion of Rees short exact sequence for Sposets is introduced, and we investigate the conditions for which these sequences are left or right split. Unlike the case for Sacts, being right split does not imply left split. Furthermore, we present equivalent conditions of a right Sposet P for the functor Hom(P;) to be exact.
1

123
134


R.
Khosravi
Department of Mathematics, Fasa University, P.O.Box 7461781189, Fasa, Iran.
Department of Mathematics, Fasa University,
Iran
khosravi@fasau.ac.ir
Sposets
pomonoids
Rees short exact sequence
projective
MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
2
2
Let $G=(V(G),E(G))$ be a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. The (first) edgehyper Wiener index of the graph $G$ is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,gG)+d_{e}^{2}(f,gG))=frac{1}{2}sum_{fin E(G)}(d_{e}(fG)+d^{2}_{e}(fG)),$$ where $d_{e}(f,gG)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $E(G)$ and $d_{e}(fG)=sum_{gin E(G)}d_{e}(f,gG)$. In this paper we use a method, which applies group theory to graph theory, to improving mathematically computation of the (first) edgehyper Wiener index in certain graphs. We give also upper and lower bounds for the (first) edgehyper 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 edgehyper Wiener index of the some classes of graphs. Our aim in last section is to find a relation between the third edgehyper Wiener index of a general graph and the hyper Wiener index of its line graph. of two or more graphs and compute edgehyper Wiener number of some classes of graphs.
1

135
153


A.
Alhevaz
Department of Mathematics, Shahrood University of Technology, P.O. Box: 316
3619995161, Shahrood, Iran.
Department of Mathematics, Shahrood University
Iran
a.alhevaz@gmail.com


M.
Baghipur
Department of Mathematics, Shahrood University of Technology, P.O. Box: 316
3619995161, Shahrood, Iran.
Department of Mathematics, Shahrood University
Iran
maryamb8989@gmail.com
Edgehyper Wiener index
line graph
Gutman index
connectivity
edgetransitive graph
THE ZERODIVISOR GRAPH OF A MODULE
2
2
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 zerodivisor graph of $R$. Many wellknown 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 zerodivisor graph of free $R$modules.
1

155
171


A.
Naghipour
Department of Mathematics, Shahrekord University, P.O. Box 115, Shahrekord,
Iran.
Department of Mathematics, Shahrekord University,
Iran
naghipourar@yahoo.com
Annilhilator
diameter
girth
reduced module
zerodivisor graph