2016
4
1
0
63
On component extensions locally compact abelian groups
2
2
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. We also gives a necessary condition for an LCA group to be component injective in $pounds$.
1

1
11


H.
Sahleh
Department of Mathematics,
University of Guilan
Department of Mathematics,
University of
Iran
sahleh@guilan.ac.ir


A. A.
Alijani
Department of Mathematics,
University of Guilan
Department of Mathematics,
University of
Iran
alijanialiakbar@gmail.com
Component extension
component injective
component projective
Homotopy approximation of modules
2
2
Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikovlike approximation of a module, with the help of a suitable set of morphisms.
1

13
20


M.
Routaray
NIT Rourkela
NIT Rourkela
India
mitaray8@gmail.com


A.
Behera
NIT Rourkela
NIT Rourkela
India
abehera@nitrkl.ac.in
Category of fractions
calculus of left fractions
Adams completion
Grothedieck universe
homotopy theory of modules
The small intersection graph relative to multiplication modules
2
2
Let $R$ be a commutative ring and let $M$ be an $R$module. We define the small intersection graph $G(M)$ of $M$ with all nonsmall proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a nonsmall submodule of $M$. In this article, we investigate the interplay between the graphtheoretic properties of $G(M)$ and algebraic properties of $M$, where $M$ is a multiplication module.
1

21
32


H.
AnsariToroghy
University of Guilan
University of Guilan
Iran
h.toroghy@gmail.com


F.
Farshadifar
University of Farhangian
University of Farhangian
Iran
f.farshadifar@gmail.com


F.
MahboobiAbkenar
University of Guilan
University of Guilan
Iran
mahboobi@phd.guilan.ac.ir
Graph
nonsmall submodule
multiplication module
Results on Hilbert coefficients of a CohenMacaulay module
2
2
Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a CohenMacaulay $R$module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal reduction of $I$.
1

33
37


A.
Mafi
University of Kurdistan
University of Kurdistan
Iran
a_mafi@ipm.ir


H.
Saremi
Islamic Azad University, Sanandaj Branch
Islamic Azad University, Sanandaj Branch
Iran
hero.saremi@gmail.com
CohenMacaulay rings
Hilbert series
Hilbert function
On zerodivisor graphs of quotient rings and complemented zerodivisor graphs
2
2
For an arbitrary ring $R$, the zerodivisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zerodivisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is wellknown that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this paper we extend this fact for certain noncommutative rings, for example, reduced rings, right (left) selfinjective rings and onesided Artinian rings. The necessary and sufficient conditions for two reduced right Goldie rings to have isomorphic zerodivisor graphs is given. Also, we extend some known results about the zerodivisor graphs from the commutative to noncommutative setting: in particular, complemented and uniquely complemented graphs.
1

39
50


P.
Karimi Beiranvand
Islamic Azad university,
Khorramabad Branch, Khorramabad
Islamic Azad university,
Khorramabad Branch,
Iran
karimi.pa@fs.lu.ac.ir


R.
Beyranvand
Lorestan University
Lorestan University
Iran
beyranvand.r@lu.ac.ir
Quotient ring
zerodivisor graph
reduced ring
complemented graph
Positive Cone in $p$Operator Projective Tensor Product of Fig`aTalamancaHerz Algebras
2
2
In this paper we define an order structure on the $p$operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.
1

51
63


M.
Shams Yousefi
A member Academic staff of university of Guilan
A member Academic staff of university of
Iran
m.shams@guilan.ac.ir
Fig`aTalamancaHerz algebra
order structure
$p$operator spaces
$p$operator projective tensor product