2018-12-11T06:51:46Z
https://jart.guilan.ac.ir/?_action=export&rf=summon&issue=362
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
1
On component extensions locally compact abelian groups
H.
Sahleh
A. A.
Alijani
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
2016
06
01
1
11
https://jart.guilan.ac.ir/article_1780_3baf91f9c2de6e444130249948b71781.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
1
Homotopy approximation of modules
M.
Routaray
A.
Behera
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
2016
06
01
13
20
https://jart.guilan.ac.ir/article_1777_53ee696b29eb2a240f54829ac2d83dd9.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
1
The small intersection graph relative to multiplication modules
H.
Ansari-Toroghy
F.
Farshadifar
F.
Mahboobi-Abkenar
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
2016
06
01
21
32
https://jart.guilan.ac.ir/article_1778_7982aca1ecb422c8fff44910661d3290.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
1
Results on Hilbert coefficients of a Cohen-Macaulay module
A.
Mafi
H.
Saremi
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
2016
06
01
33
37
https://jart.guilan.ac.ir/article_1782_30576b5a834b8dd9eb6c4546fb7d4f34.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
1
On zero-divisor graphs of quotient rings and complemented zero-divisor graphs
P.
Karimi Beiranvand
R.
Beyranvand
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
2016
06
01
39
50
https://jart.guilan.ac.ir/article_1781_38d9e44bdeda75362869943f4e3b1c63.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2016
4
1
Positive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras
M.
Shams Yousefi
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
2016
06
01
51
63
https://jart.guilan.ac.ir/article_1783_6033818f49a2c9b0aac2e0088b34fdcd.pdf