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Local-Global Theory over Regular Domains of Dimension Two

✍ Scribed by R. Wiegand

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 631 KB
Volume: 155
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1993.1056

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📜 SIMILAR VOLUMES

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Let R, m, K be a regular local ring of dimension n and let M be a finite length module over R. This paper gives an affirmative answer to Horrocks' questions when m 2 M s 0, that is, in this case the rank of the ith syzygy of M is at and the ith Betti number of M is at least .

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This paper explicitly determines the core of a torsion-free, integrally closed module over a two-dimensional regular local ring. It is analogous to a result of Huneke and Swanson which determines the core of an integrally closed ideal. The main result asserts that the core of a finitely generated, t