فهرست مطالب
Journal of Algebra and Related Topics
Volume:4 Issue: 1, Summer 2016
- تاریخ انتشار: 1395/04/28
- تعداد عناوین: 6
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Pages 1-11et \pounds be the category of locally compact abelian groups and A,C∈\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
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Pages 13-20Deleanu, 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
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Pages 21-32Let 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∩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 Mis a multiplication module.Keywords: Graph, non, small submodule, multiplication module
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Pages 33-37Let (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 λ(InM˜JIn−1M˜) does not depend on J for all n≥1, where J is a minimal reduction of I.Keywords: Cohen, Macaulay rings, Hilbert series, Hilbert function
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Pages 39-50For an arbitrary ring R, the zero-divisor graph of R, denoted by Γ(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, Γ(R)≅Γ(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 -
Pages 51-63In 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 Ap(G×H) and Ap(G)⊗pAp(H) is an order isomorphism for amenable groups G and H.Keywords: Figa, Talamanca, Herz algebra, order structure, p, operator spaces, p, operator projective tensor product