منابع مشابه
Sally Modules and Associated Graded Rings
To frame and motivate the goals pursued in the present article we recall that, loosely speaking, the most common among the blowup algebras are the Rees algebra R[It] = ⊕∞ n=0 I ntn and the associated graded ring grI(R) = ⊕∞ n=0 I n/In+1 of an ideal I in a commutative Noetherian local ring (R,m). The three main clusters around which most of the current research on blowup algebras has been develo...
متن کاملGraded Rings and Modules
1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...
متن کاملAssociated Graphs of Modules Over Commutative Rings
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...
متن کاملTight Closure of Finite Length Modules in Graded Rings
In this article, we look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our result does not depend upon dimension, the primary application is based on results known in dimension 2 due to the recent work of H. Brenner...
متن کاملGraded Rings Associated with Contracted Ideals
The study of the ideals in a regular local ring (R,m) of dimension 2 has a long and important tradition dating back to the fundamental work of Zariski [ZS]. More recent contributions are due to several authors including Cutkosky, Huneke, Lipman, Sally and Tessier among others, see [C1, C2, H, HS, L, LT]. One of the main result in this setting is the unique factorization theorem for complete (i....
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 1998
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927879808826304