University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
4
1
2016
06
01
On component extensions locally compact abelian groups
1
11
EN
H.
Sahleh
Department of Mathematics,
University of Guilan
sahleh@guilan.ac.ir
A. A.
Alijani
Department of Mathematics,
University of Guilan
alijanialiakbar@gmail.com
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 $pounds$.
Component extension,component injective,component projective
https://jart.guilan.ac.ir/article_1780.html
https://jart.guilan.ac.ir/article_1780_3baf91f9c2de6e444130249948b71781.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
4
1
2016
06
01
Homotopy approximation of modules
13
20
EN
M.
Routaray
NIT Rourkela
mitaray8@gmail.com
A.
Behera
NIT Rourkela
abehera@nitrkl.ac.in
Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.
Category of fractions,calculus of left fractions,Adams completion,Grothedieck
universe,homotopy theory of modules
https://jart.guilan.ac.ir/article_1777.html
https://jart.guilan.ac.ir/article_1777_53ee696b29eb2a240f54829ac2d83dd9.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
4
1
2016
06
01
The small intersection graph relative to multiplication modules
21
32
EN
H.
Ansari-Toroghy
University of Guilan
h.toroghy@gmail.com
F.
Farshadifar
University of Farhangian
f.farshadifar@gmail.com
F.
Mahboobi-Abkenar
University of Guilan
mahboobi@phd.guilan.ac.ir
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 non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M$, where $M$ is a multiplication module.
Graph,non-small submodule,multiplication module
https://jart.guilan.ac.ir/article_1778.html
https://jart.guilan.ac.ir/article_1778_7982aca1ecb422c8fff44910661d3290.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
4
1
2016
06
01
Results on Hilbert coefficients of a Cohen-Macaulay module
33
37
EN
A.
Mafi
University of Kurdistan
a_mafi@ipm.ir
H.
Saremi
Islamic Azad University, Sanandaj Branch
hero.saremi@gmail.com
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 Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal reduction of $I$.
Cohen-Macaulay rings,Hilbert series,Hilbert function
https://jart.guilan.ac.ir/article_1782.html
https://jart.guilan.ac.ir/article_1782_30576b5a834b8dd9eb6c4546fb7d4f34.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
4
1
2016
06
01
On zero-divisor graphs of quotient rings and complemented zero-divisor graphs
39
50
EN
P.
Karimi Beiranvand
Islamic Azad university,
Khorramabad Branch, Khorramabad
karimi.pa@fs.lu.ac.ir
R.
Beyranvand
Lorestan University
beyranvand.r@lu.ac.ir
For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known 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) self-injective rings and one-sided Artinian rings. The necessary and sufficient conditions for two reduced right Goldie rings to have isomorphic zero-divisor graphs is given. Also, we extend some known results about the zero-divisor graphs from the commutative to noncommutative setting: in particular, complemented and uniquely complemented graphs.
Quotient ring,zero-divisor graph,reduced ring,complemented graph
https://jart.guilan.ac.ir/article_1781.html
https://jart.guilan.ac.ir/article_1781_38d9e44bdeda75362869943f4e3b1c63.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
4
1
2016
06
01
Positive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras
51
63
EN
M.
Shams Yousefi
A member Academic staff of university of Guilan
m.shams@guilan.ac.ir
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 $H$.
Fig`a-Talamanca-Herz algebra,order structure,$p$-operator spaces,$p$-operator projective tensor
product
https://jart.guilan.ac.ir/article_1783.html
https://jart.guilan.ac.ir/article_1783_6033818f49a2c9b0aac2e0088b34fdcd.pdf