Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 2 2017 01 01 FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES 85 95 850 10.22044/jas.2017.850 EN M. Rezaei Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. Z. Foruzanfar Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. Journal Article 2015 04 20 ‎Let G be a finite group and Z(G) be the center of G‎. ‎For a subset A of G‎, ‎we define k<sub>G</sub>(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 k<sub>G</sub>(G-Z(G))=5, and classify them‎.
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 2 2017 01 01 FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS 97 101 851 10.22044/jas.2017.851 EN F. Forouzesh Faculty of Mathematics and Computing, Higher Education Complex of Bam, Ker- man, Iran Journal Article 2015 04 23 In this paper, we introduce the notion of fuzzy obstinate ideals in MV -algebras. Some properties of fuzzy obstinate<br />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 <em>Μ </em>is a fuzzy obstinate ideal of A such that <em>M</em>(0) 2 [0; 1=2], then A=<em>Μ </em>is a Boolean algebra. Finally, we define the notion of a normal fuzzy obstinate ideal and investigate some of its properties.
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 2 2017 01 01 RADICAL OF FILTERS IN RESIDUATED LATTICES 111 121 852 10.22044/jas.2017.852 EN S. Motamed Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran. Journal Article 2016 01 31 ‎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.
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 2 2017 01 01 REES SHORT EXACT SEQUENCES OF S-POSETS 123 134 853 10.22044/jas.2017.853 EN R. Khosravi Department of Mathematics, Fasa University, P.O.Box 74617-81189, Fasa, Iran. Journal Article 2016 02 03 In this paper the notion of Rees short exact sequence for S-posets<br /> is introduced, and we investigate the conditions for which these sequences are left or right split. Unlike the case for S-acts,<br /> being right split does not imply left split. Furthermore, we present<br /> equivalent conditions of a right S-poset P for the functor Hom(P;-)<br /> to be exact.
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 2 2017 01 01 MORE ON EDGE HYPER WIENER INDEX OF GRAPHS 135 153 854 10.22044/jas.2017.854 EN A. Alhevaz Department of Mathematics, Shahrood University of Technology, P.O. Box: 316- 3619995161, Shahrood, Iran. 0000-0001-6167-607X M. Baghipur Department of Mathematics, Shahrood University of Technology, P.O. Box: 316- 3619995161, Shahrood, Iran. 0000-0002-9069-9243 Journal Article 2016 04 10 ‎Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge‎<br /> ‎set E(G)‎. ‎The (first) edge-hyper Wiener index of the graph G is defined as‎:<br /> ‎\$\$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)),\$\$‎<br /> ‎where d<sub>e</sub>(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and d<sub>e</sub>(f|G)=∑<sub><span style="font-size: 8.33333px;">g€(G)</span></sub><span style="font-size: 8.33333px;">d<sub>e</sub>(f,g|G).</span><br /> ‎In this paper we use a method‎, ‎which applies group theory to graph theory‎, ‎to improving‎<br /> ‎mathematically computation of the (first) edge-hyper Wiener index in certain graphs‎.<br /> ‎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.<br /> ‎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.
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 2 2017 01 01 THE ZERO-DIVISOR GRAPH OF A MODULE 155 171 858 10.22044/jas.2017.858 EN A. Naghipour Department of Mathematics, Shahrekord University, P.O. Box 115, Shahrekord, Iran. 0000-0002-7178-6173 Journal Article 2016 12 04 Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say<br />Γ(RM), such that when M=R, Γ(<sub>R</sub>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 Γ(RM). We Will show that Γ(<sub>R</sub>M) is connected with<br />diam 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 a<br />prime module. Among other results, it is shown that for a reduced module M satisfying DCC on cyclic submodules,<br />gr (Γ(RM))=∞ if and only if Γ(RM) is a star graph. Finally, we study the zero-divisor graph of free<br />R-modules.