eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-01-01
4
2
85
95
10.22044/jas.2017.850
850
FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES
M. Rezaei
mehdrezaei@gmail.com
1
Z. Foruzanfar
zforouzanfar@gmail.com
2
Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.
Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.
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.
http://jas.shahroodut.ac.ir/article_850_f26adfb749347531a3cb078626440a73.pdf
Finite group
Frobenius group
Conjugacy class
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-01-01
4
2
97
101
10.22044/jas.2017.851
851
FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS
F. Forouzesh
ffrouzesh@yahoo.com
1
Faculty of Mathematics and Computing, Higher Education Complex of Bam, Ker- man, Iran
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.
http://jas.shahroodut.ac.ir/article_851_08ccea2270f1cc3558fbf666ad8998c9.pdf
MV-algebra
fuzzy normal
fuzzy obstinate
fuzzy Boolean
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-01-01
4
2
111
121
10.22044/jas.2017.852
852
RADICAL OF FILTERS IN RESIDUATED LATTICES
S. Motamed
somayeh.motamed@iauba.ac.ir
1
Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.
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.
http://jas.shahroodut.ac.ir/article_852_9a18ec2a81ec3a16def3083c7ce891e7.pdf
(Maximal) Prime filter
Radical
Residuated lattice
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-01-01
4
2
123
134
10.22044/jas.2017.853
853
REES SHORT EXACT SEQUENCES OF S-POSETS
R. Khosravi
khosravi@fasau.ac.ir
1
Department of Mathematics, Fasa University, P.O.Box 74617-81189, Fasa, Iran.
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.
http://jas.shahroodut.ac.ir/article_853_51ae2012410695a2524b1b1489d9be5d.pdf
S-posets
pomonoids
Rees short exact sequence
projective
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-01-01
4
2
135
153
10.22044/jas.2017.854
854
MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
A. Alhevaz
a.alhevaz@gmail.com
1
M. Baghipur
maryamb8989@gmail.com
2
Department of Mathematics, Shahrood University of Technology, P.O. Box: 316- 3619995161, Shahrood, Iran.
Department of Mathematics, Shahrood University of Technology, P.O. Box: 316- 3619995161, Shahrood, Iran.
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.
http://jas.shahroodut.ac.ir/article_854_2486403d0b8da2a0bb248f7cd1fcd96b.pdf
Edge-hyper Wiener index
line graph
Gutman index
connectivity
edge-transitive graph
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-01-01
4
2
155
171
10.22044/jas.2017.858
858
THE ZERO-DIVISOR GRAPH OF A MODULE
A. Naghipour
naghipourar@yahoo.com
1
Department of Mathematics, Shahrekord University, P.O. Box 115, Shahrekord, Iran.
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.
http://jas.shahroodut.ac.ir/article_858_dc9a03e1918e0e0bd28530d1103281ff.pdf
Annilhilator
diameter
girth
reduced module
zero-divisor graph