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New Invariants of Noetherian Local Rings

✍ Scribed by Jee Koh; Kisuk Lee

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 158 KB
Volume: 235
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8506

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✦ Synopsis

We investigate properties of certain invariants of Noetherian local rings, including their behavior under flat local homomorphisms. We show that these invariants are bounded by the multiplicity for Cohen-Macaulay local rings with infinite residue fields, and they all agree with the multiplicity when such rings are hypersurfaces. We also show that these invariants are all equal to 2 for a non-regular Cohen-Macaulay local ring A if and only if A has a minimal multiplicity, provided its residue field is infinite.

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