On the canonical element conjecture. II
type: Item
instance of: scholarly article
title: On the canonical element conjecture. II
zbMATH Open document ID: 0806.13002
DOI: 10.1007/BF02572328
published in: Mathematische Zeitschrift
publication date: 1994-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174657
review text: [For part I see Trans. Am. Math. Soc. 299, 803-811 (1987; Zbl 0611.13011).] The main two theorems of this paper are the following: Theorem 1. Let \((A,m,k)\) be a noetherian local ring and let \(J_ i = \text{ann}_ A H_ m^{n-i} (A)\). Then for any nonzero \(x \in mJ_ 1J_ 2 \dots J_ r\), \(A/xA\) satisfies the canonical element conjecture (here \(r = \dim A - \text{depth} A)\). Theorem 2. Let \(x_ n \in J_ 1J_ 2 \dots J_ r\). Then for any s.o.p. \(x_ 1, x_ 2, \dots, x_ n\) of \(A\), \(x^ t_ 1, x_ 2^ t, \dots, x^ t_ n + x\) satisfies the canonical element conjecture in \(B = AX/(X^ 2)\) \((x\) denoting the image of \(X\) in \(B)\) for every positive integer \(t\).
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 13H05
zbMATH DE Number: 704924
zbMATH Keywords: formal power series
zbMATH Keywords: noetherian local ring
zbMATH Keywords: canonical element conjecture
author: S. P. Dutta
MaRDI profile type: Publication
Wikidata QID: Q122902007
cites work: Q3360288
cites work: Canonical elements in local cohomology modules and the direct summand conjecture
cites work: The Poincaré series of a local ring
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description: scientific article; zbMATH DE number 704924