Quasi-Regular Sequences and Regular Sequences

Cherrabi, A.

doi:10.1080/00927870903451942

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A Characterization Of Cohen-macaulay Modules1

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2014

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“…The main goals of this section are Theorems 2.3, 2.4 and 2.7. The following lemma, which is a generalization of [4,Proposition 1.4], is needed in the proof of Lemma 2.2.…”

Section: A Characterization Of Cohen-macaulay Modulesmentioning

confidence: 99%

Cohen-Macaulay Modules Over Noetherian Local Rings

Bahmanpour¹

2014

Bulletin of the Korean Mathematical Society

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Abstract. Let (R, m) be a commutative Noetherian local ring. In this paper we show that a finitely generated R-module M of dimension d is Cohen-Macaulay if and only if there exists a proper ideal I of R such that depth(M/I n M ) = d for n ≫ 0. Also we show that, if dim(R) = d and I 1 ⊂ · · · ⊂ In is a chain of ideals of R such that R/I k is maximal Cohen-Macaulay for all k, then n ≤ ℓ R (R/(a 1 , . . . , a d )R) for every system of parameters a 1 , . . . , a d of R. Also, in the case where dim(R) = 2, we prove that the ideal transform Dm(R/ p) is minimax balanced big Cohen-Macaulay, for every p ∈ Assh R (R), and we give some equivalent conditions for this ideal transform being maximal Cohen-Macaulay.

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“…The main goals of this section are Theorems 2.3, 2.4 and 2.7. The following lemma, which is a generalization of [4,Proposition 1.4], is needed in the proof of Lemma 2.2.…”

Section: A Characterization Of Cohen-macaulay Modulesmentioning

confidence: 99%

Cohen-Macaulay Modules Over Noetherian Local Rings

Bahmanpour¹

2014

Bulletin of the Korean Mathematical Society

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show abstract

Quasi-Regular Sequences and Regular Sequences

Cited by 1 publication

References 4 publications

Cohen-Macaulay Modules Over Noetherian Local Rings

Cohen-Macaulay Modules Over Noetherian Local Rings

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