Shahrood University of TechnologyJournal of Algebraic Systems2345-51284220170101FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES859585010.22044/jas.2017.850ENM. RezaeiDepartment of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.0000-0001-6999-9703Z. ForuzanfarBuein Zahra Technical University, Buein Zahra, Qazvin, Iran.0000-0002-8585-9636Journal Article20150420Let 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.https://jas.shahroodut.ac.ir/article_850_f26adfb749347531a3cb078626440a73.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51284220170101FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS9710185110.22044/jas.2017.851ENF. ForouzeshFaculty of Mathematics and Computing, Higher Education Complex of Bam, Ker-
man, IranJournal Article20150423In 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.https://jas.shahroodut.ac.ir/article_851_08ccea2270f1cc3558fbf666ad8998c9.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51284220170101RADICAL OF FILTERS IN RESIDUATED LATTICES11112185210.22044/jas.2017.852ENS. MotamedDepartment of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.Journal Article20160131In 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.https://jas.shahroodut.ac.ir/article_852_9a18ec2a81ec3a16def3083c7ce891e7.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51284220170101REES SHORT EXACT SEQUENCES OF S-POSETS12313485310.22044/jas.2017.853ENR. KhosraviDepartment of Mathematics, Fasa University, P.O.Box 74617-81189, Fasa, Iran.Journal Article20160203In 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.https://jas.shahroodut.ac.ir/article_853_51ae2012410695a2524b1b1489d9be5d.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51284220170101MORE ON EDGE HYPER WIENER INDEX OF GRAPHS13515385410.22044/jas.2017.854ENA. AlhevazDepartment of Mathematics, Shahrood University of Technology, P.O. Box: 316-
3619995161, Shahrood, Iran.0000-0001-6167-607XM. BaghipurDepartment of Mathematics, Shahrood University of Technology, P.O. Box: 316-
3619995161, Shahrood, Iran.0000-0002-9069-9243Journal Article20160410Let 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 /> $$WW_{e}(G)=\sum_{\{f,g\}\subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=\frac{1}{2}\sum_{f\in E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$<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.https://jas.shahroodut.ac.ir/article_854_2486403d0b8da2a0bb248f7cd1fcd96b.pdfShahrood University of TechnologyJournal of Algebraic Systems2345-51284220170101THE ZERO-DIVISOR GRAPH OF A MODULE15517185810.22044/jas.2017.858ENA. NaghipourDepartment of Mathematics, Shahrekord University, P.O. Box 115, Shahrekord,
Iran.0000-0002-7178-6173Journal Article20161204Let 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. https://jas.shahroodut.ac.ir/article_858_dc9a03e1918e0e0bd28530d1103281ff.pdf