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 kG(A), the number of conjugacy classes of G that intersect A non-trivially. In this paper, we verify the structure of all finite groups G which satisfy the property kG(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
In this paper, we introduce the notion of fuzzy obstinate ideals in MV -algebras. Some properties of fuzzy obstinateideals 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 Μ is a fuzzy obstinate ideal of A such that M(0) 2 [0; 1=2], then A=Μ is a Boolean algebra. Finally, we define the notion of a normal fuzzy obstinate ideal and investigate some of its 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 de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(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, sayΓ(RM), such that when M=R, Γ(RM) coincide with the zero-divisor graph of R. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for Γ(RM). We Will show that Γ(RM) is connected withdiam Γ(RM)≤ 3 and if Γ(RM) contains a cycle, then Γ(RM)≤4. We will also show that Γ(RM)=Ø if and only if M is aprime module. Among other results, it is shown that for a reduced module M satisfying DCC on cyclic submodules,gr (Γ(RM))=∞ if and only if Γ(RM) is a star graph. Finally, we study the zero-divisor graph of freeR-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