@Article{Rezaei2017,
author="Rezaei, M.
and Foruzanfar, Z.",
title="FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES",
journal="Journal of Algebraic Systems",
year="2017",
volume="4",
number="2",
pages="85-95",
abstract="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.",
issn="2345-5128",
doi="10.22044/jas.2017.850",
url="http://jas.shahroodut.ac.ir/article_850.html"
}
@Article{Forouzesh2017,
author="Forouzesh, F.",
title="FUZZY OBSTINATE IDEALS IN MV-ALGEBRAS",
journal="Journal of Algebraic Systems",
year="2017",
volume="4",
number="2",
pages="97-101",
abstract="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.",
issn="2345-5128",
doi="10.22044/jas.2017.851",
url="http://jas.shahroodut.ac.ir/article_851.html"
}
@Article{Motamed2017,
author="Motamed, S.",
title="RADICAL OF FILTERS IN RESIDUATED LATTICES",
journal="Journal of Algebraic Systems",
year="2017",
volume="4",
number="2",
pages="111-121",
abstract="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.",
issn="2345-5128",
doi="10.22044/jas.2017.852",
url="http://jas.shahroodut.ac.ir/article_852.html"
}
@Article{Khosravi2017,
author="Khosravi, R.",
title="REES SHORT EXACT SEQUENCES OF S-POSETS",
journal="Journal of Algebraic Systems",
year="2017",
volume="4",
number="2",
pages="123-134",
abstract="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.",
issn="2345-5128",
doi="10.22044/jas.2017.853",
url="http://jas.shahroodut.ac.ir/article_853.html"
}
@Article{Alhevaz2017,
author="Alhevaz, A.
and Baghipur, M.",
title="MORE ON EDGE HYPER WIENER INDEX OF GRAPHS",
journal="Journal of Algebraic Systems",
year="2017",
volume="4",
number="2",
pages="135-153",
abstract="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.",
issn="2345-5128",
doi="10.22044/jas.2017.854",
url="http://jas.shahroodut.ac.ir/article_854.html"
}
@Article{Naghipour2017,
author="Naghipour, A.",
title="THE ZERO-DIVISOR GRAPH OF A MODULE",
journal="Journal of Algebraic Systems",
year="2017",
volume="4",
number="2",
pages="155-171",
abstract="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. ",
issn="2345-5128",
doi="10.22044/jas.2017.858",
url="http://jas.shahroodut.ac.ir/article_858.html"
}