@Article{Sahleh2016,
author="Sahleh, H.
and Alijani, A. A.",
title="On component extensions locally compact abelian groups",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="1",
pages="1-11",
abstract="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 $\pounds$.",
issn="2345-3931",
doi="",
url="http://jart.guilan.ac.ir/article_1780.html"
}
@Article{Routaray2016,
author="Routaray, M.
and Behera, A.",
title="Homotopy approximation of modules",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="1",
pages="13-20",
abstract="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.",
issn="2345-3931",
doi="",
url="http://jart.guilan.ac.ir/article_1777.html"
}
@Article{Ansari-Toroghy2016,
author="Ansari-Toroghy, H.
and Farshadifar, F.
and Mahboobi-Abkenar, F.",
title="The small intersection graph relative to multiplication modules",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="1",
pages="21-32",
abstract="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.",
issn="2345-3931",
doi="",
url="http://jart.guilan.ac.ir/article_1778.html"
}
@Article{Mafi2016,
author="Mafi, A.
and Saremi, H.",
title="Results on Hilbert coefficients of a Cohen-Macaulay module",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="1",
pages="33-37",
abstract="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 $I$.",
issn="2345-3931",
doi="",
url="http://jart.guilan.ac.ir/article_1782.html"
}
@Article{KarimiBeiranvand2016,
author="Karimi Beiranvand, P.
and Beyranvand, R.",
title="On zero-divisor graphs of quotient rings and complemented zero-divisor graphs",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="1",
pages="39-50",
abstract="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.",
issn="2345-3931",
doi="",
url="http://jart.guilan.ac.ir/article_1781.html"
}
@Article{ShamsYousefi2016,
author="Shams Yousefi, M.",
title="Positive Cone in $p$-Operator Projective Tensor Product of Fig\`a-Talamanca-Herz Algebras",
journal="Journal of Algebra and Related Topics",
year="2016",
volume="4",
number="1",
pages="51-63",
abstract="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 $H$.",
issn="2345-3931",
doi="",
url="http://jart.guilan.ac.ir/article_1783.html"
}