@article { author = {Sahleh, H. and Alijani, A. A.}, title = {On component extensions locally compact abelian groups}, journal = {Journal of Algebra and Related Topics}, volume = {4}, number = {1}, pages = {1-11}, year = {2016}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, 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 $\pounds$.}, keywords = {Component extension,component injective,component projective}, url = {https://jart.guilan.ac.ir/article_1780.html}, eprint = {https://jart.guilan.ac.ir/article_1780_3baf91f9c2de6e444130249948b71781.pdf} } @article { author = {Routaray, M. and Behera, A.}, title = {Homotopy approximation of modules}, journal = {Journal of Algebra and Related Topics}, volume = {4}, number = {1}, pages = {13-20}, year = {2016}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, 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.}, keywords = {Category of fractions,calculus of left fractions,Adams completion,Grothedieck universe,homotopy theory of modules}, url = {https://jart.guilan.ac.ir/article_1777.html}, eprint = {https://jart.guilan.ac.ir/article_1777_53ee696b29eb2a240f54829ac2d83dd9.pdf} } @article { 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}, volume = {4}, number = {1}, pages = {21-32}, year = {2016}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2016.1778}, 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.}, keywords = {Graph,non-small submodule,multiplication module}, url = {https://jart.guilan.ac.ir/article_1778.html}, eprint = {https://jart.guilan.ac.ir/article_1778_7982aca1ecb422c8fff44910661d3290.pdf} } @article { author = {Mafi, A. and Saremi, H.}, title = {Results on Hilbert coefficients of a Cohen-Macaulay module}, journal = {Journal of Algebra and Related Topics}, volume = {4}, number = {1}, pages = {33-37}, year = {2016}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, 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 $I$.}, keywords = {Cohen-Macaulay rings,Hilbert series,Hilbert function}, url = {https://jart.guilan.ac.ir/article_1782.html}, eprint = {https://jart.guilan.ac.ir/article_1782_30576b5a834b8dd9eb6c4546fb7d4f34.pdf} } @article { 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}, volume = {4}, number = {1}, pages = {39-50}, year = {2016}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, 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.}, keywords = {Quotient ring,zero-divisor graph,reduced ring,complemented graph}, url = {https://jart.guilan.ac.ir/article_1781.html}, eprint = {https://jart.guilan.ac.ir/article_1781_38d9e44bdeda75362869943f4e3b1c63.pdf} } @article { 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}, volume = {4}, number = {1}, pages = {51-63}, year = {2016}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {}, 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 $H$.}, keywords = {Fig`a-Talamanca-Herz algebra,order structure,$p$-operator spaces,$p$-operator projective tensor product}, url = {https://jart.guilan.ac.ir/article_1783.html}, eprint = {https://jart.guilan.ac.ir/article_1783_6033818f49a2c9b0aac2e0088b34fdcd.pdf} }