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2008•Algebra ColloquiumRequires access

Top Local Cohomology Modules with Specified Attached Primes

Mohammad T. Dibaei, Raheleh Jafari

Open publisher page 7 citations

Abstract

Let (R, 𝔪) be a complete Noetherian local ring and let M be a finite R-module of positive Krull dimension n. It is shown that any subset T of Assh R(M) can be expressed as the set of attached primes of the top local cohomology module [Formula: see text] for some ideal 𝔞 of R. Moreover, if 𝔞 is an ideal of R such that the set of attached primes of [Formula: see text] is a non-empty proper subset of Assh R(M), then [Formula: see text] for some ideal 𝔟 of R with dim R(R/𝔟) = 1.

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What this paper is about

Let (R, 𝔪) be a complete Noetherian local ring and let M be a finite R-module of positive Krull dimension n. It is shown that any subset T of Assh R(M) can be expressed as the set of attached primes of the top local cohomology module [Formula: see text] for some ideal 𝔞 of R. Moreover, if 𝔞 is an ideal of R such that the set of attached primes of [Formula: see text] is a non-empty proper subset of Assh R(M), then [Formula: see text] for some ideal 𝔟 of R with dim R(R/𝔟) = 1.

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Available abstract

Let (R, 𝔪) be a complete Noetherian local ring and let M be a finite R-module of positive Krull dimension n. It is shown that any subset T of Assh R(M) can be expressed as the set of attached primes of the top local cohomology module [Formula: see text] for some ideal 𝔞 of R. Moreover, if 𝔞 is an ideal of R such that the set of attached primes of [Formula: see text] is a non-empty proper subset of Assh R(M), then [Formula: see text] for some ideal 𝔟 of R with dim R(R/𝔟) = 1.

Key concepts: Local cohomology, Mathematics, Krull dimension, Ideal (ethics), Regular local ring, Noetherian ring, Noetherian, Maximal ideal

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