Journal of Algebraic SystemsJournal of Algebraic Systems
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Feed provided by Journal of Algebraic Systems. Click to visit.FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES
http://jas.shahroodut.ac.ir/article_850_100.html
‎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.Sat, 31 Dec 2016 20:30:00 +0100FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS
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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.Sat, 31 Dec 2016 20:30:00 +0100RADICAL OF FILTERS IN RESIDUATED LATTICES
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‎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.Sat, 31 Dec 2016 20:30:00 +0100REES SHORT EXACT SEQUENCES OF S-POSETS
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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.Sat, 31 Dec 2016 20:30:00 +0100MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
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‎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.Sat, 31 Dec 2016 20:30:00 +0100THE ZERO-DIVISOR GRAPH OF A MODULE
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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.Sat, 31 Dec 2016 20:30:00 +0100A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS
http://jas.shahroodut.ac.ir/article_882_0.html
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.Mon, 20 Feb 2017 20:30:00 +0100