2017-08-22T11:51:23Z
http://jas.shahroodut.ac.ir/?_action=export&rf=summon&issue=117
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2017
4
2
FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES
M.
Rezaei
Z.
Foruzanfar
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
2017
01
01
85
95
http://jas.shahroodut.ac.ir/article_850_f26adfb749347531a3cb078626440a73.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2017
4
2
FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS
F.
Forouzesh
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
2017
01
01
97
101
http://jas.shahroodut.ac.ir/article_851_08ccea2270f1cc3558fbf666ad8998c9.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2017
4
2
RADICAL OF FILTERS IN RESIDUATED LATTICES
S.
Motamed
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
2017
01
01
111
121
http://jas.shahroodut.ac.ir/article_852_9a18ec2a81ec3a16def3083c7ce891e7.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2017
4
2
REES SHORT EXACT SEQUENCES OF S-POSETS
R.
Khosravi
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
2017
01
01
123
134
http://jas.shahroodut.ac.ir/article_853_51ae2012410695a2524b1b1489d9be5d.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2017
4
2
MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
A.
Alhevaz
M.
Baghipur
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
2017
01
01
135
153
http://jas.shahroodut.ac.ir/article_854_2486403d0b8da2a0bb248f7cd1fcd96b.pdf
Journal of Algebraic Systems
JAS
2345-5128
2345-5128
2017
4
2
THE ZERO-DIVISOR GRAPH OF A MODULE
A.
Naghipour
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
2017
01
01
155
171
http://jas.shahroodut.ac.ir/article_858_dc9a03e1918e0e0bd28530d1103281ff.pdf