On component extensions locally compact abelian groups
H.
Sahleh
Department of Mathematics,
University of Guilan
author
A. A.
Alijani
Department of Mathematics,
University of Guilan
author
text
article
2016
eng
Let $\pounds$ be the category of locally compact abelian groups and $A,C\in \pounds$. 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 $\pounds$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
1
no.
2016
1
11
https://jart.guilan.ac.ir/article_1780_3baf91f9c2de6e444130249948b71781.pdf
Homotopy approximation of modules
M.
Routaray
NIT Rourkela
author
A.
Behera
NIT Rourkela
author
text
article
2016
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
1
no.
2016
13
20
https://jart.guilan.ac.ir/article_1777_53ee696b29eb2a240f54829ac2d83dd9.pdf
The small intersection graph relative to multiplication modules
H.
Ansari-Toroghy
University of Guilan
author
F.
Farshadifar
University of Farhangian
author
F.
Mahboobi-Abkenar
University of Guilan
author
text
article
2016
eng
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 $N\cap K$ 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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
1
no.
2016
21
32
https://jart.guilan.ac.ir/article_1778_7982aca1ecb422c8fff44910661d3290.pdf
Results on Hilbert coefficients of a Cohen-Macaulay module
A.
Mafi
University of Kurdistan
author
H.
Saremi
Islamic Azad University, Sanandaj Branch
author
text
article
2016
eng
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 $\lambda(\frac{\widetilde{I^nM}}{J\widetilde{I^{n-1}M}})$ does not depend on $J$ for all $n\geq 1$, where $J$ is a minimal reduction of $I$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
1
no.
2016
33
37
https://jart.guilan.ac.ir/article_1782_30576b5a834b8dd9eb6c4546fb7d4f34.pdf
On zero-divisor graphs of quotient rings and complemented zero-divisor graphs
P.
Karimi Beiranvand
Islamic Azad university,
Khorramabad Branch, Khorramabad
author
R.
Beyranvand
Lorestan University
author
text
article
2016
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
1
no.
2016
39
50
https://jart.guilan.ac.ir/article_1781_38d9e44bdeda75362869943f4e3b1c63.pdf
Positive Cone in $p$-Operator Projective Tensor Product of Fig\`a-Talamanca-Herz Algebras
M.
Shams Yousefi
A member Academic staff of university of Guilan
author
text
article
2016
eng
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 $A_p(G\times H)$ and $A_p(G)\widehat{\otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
4
v.
1
no.
2016
51
63
https://jart.guilan.ac.ir/article_1783_6033818f49a2c9b0aac2e0088b34fdcd.pdf