FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES M. Rezaei Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. author Z. Foruzanfar Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. author text article 2017 eng ‎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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 4 v. 2 no. 2017 85 95 http://jas.shahroodut.ac.ir/article_850_f26adfb749347531a3cb078626440a73.pdf dx.doi.org/10.22044/jas.2017.850 FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS F. Forouzesh Faculty of Mathematics and Computing, Higher Education Complex of Bam, Ker- man, Iran author text article 2017 eng 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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 4 v. 2 no. 2017 97 101 http://jas.shahroodut.ac.ir/article_851_08ccea2270f1cc3558fbf666ad8998c9.pdf dx.doi.org/10.22044/jas.2017.851 RADICAL OF FILTERS IN RESIDUATED LATTICES S. Motamed Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran. author text article 2017 eng ‎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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 4 v. 2 no. 2017 111 121 http://jas.shahroodut.ac.ir/article_852_9a18ec2a81ec3a16def3083c7ce891e7.pdf dx.doi.org/10.22044/jas.2017.852 REES SHORT EXACT SEQUENCES OF S-POSETS R. Khosravi Department of Mathematics, Fasa University, P.O.Box 74617-81189, Fasa, Iran. author text article 2017 eng 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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 4 v. 2 no. 2017 123 134 http://jas.shahroodut.ac.ir/article_853_51ae2012410695a2524b1b1489d9be5d.pdf dx.doi.org/10.22044/jas.2017.853 MORE ON EDGE HYPER WIENER INDEX OF GRAPHS A. Alhevaz Department of Mathematics, Shahrood University of Technology, P.O. Box: 316- 3619995161, Shahrood, Iran. author M. Baghipur Department of Mathematics, Shahrood University of Technology, P.O. Box: 316- 3619995161, Shahrood, Iran. author text article 2017 eng ‎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: ‎$$WW_{e}(G)=\sum_{\{f,g\}\subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=\frac{1}{2}\sum_{f\in E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$‎ ‎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. Journal of Algebraic Systems Shahrood University of Technology 2345-5128 4 v. 2 no. 2017 135 153 http://jas.shahroodut.ac.ir/article_854_2486403d0b8da2a0bb248f7cd1fcd96b.pdf dx.doi.org/10.22044/jas.2017.854 THE ZERO-DIVISOR GRAPH OF A MODULE A. Naghipour Department of Mathematics, Shahrekord University, P.O. Box 115, Shahrekord, Iran. author text article 2017 eng 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.  Journal of Algebraic Systems Shahrood University of Technology 2345-5128 4 v. 2 no. 2017 155 171 http://jas.shahroodut.ac.ir/article_858_dc9a03e1918e0e0bd28530d1103281ff.pdf dx.doi.org/10.22044/jas.2017.858