منابع مشابه
Periodic modules over Gorenstein local rings
It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t ±1 ]-module associated to R. This module, denoted J(R), is the free Z[t ±1 ]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The ...
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Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...
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In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...
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6 We give a new criterion for a commutative, noetherian, local ring to be CohenMacaulay. Additionally, we present a class of chain complexes of finitely generated free modules with finite length homology whose existence in the most general setting is crucial to the validity of the Improved New Intersection Conjecture.
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We prove that for modules M and N over a local ring R, the depth formula: depthR M + depthR N − depthR = depthR Tor R s (M,N) − s, where s = sup{i | Tor i (M,N) 6= 0}, holds under certain conditions. This adds to the list cases where the depth formula, which extends the classical Auslander-Buchsbaum equality, is satisfied.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8694