New Invariants of Noetherian Local Rings

Authors: Koh J.^{1, 2}; Lee K.³

Source: Journal of Algebra, Volume 235, Number 2, January 2001 , pp. 431-452(22)

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Abstract:

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. Copyright 2001 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, Indiana University, Bloomington, Indiana, 47405 2: School of Mathematics, Korea Institute for Advanced Study, Seoul, Korea 3: Department of Mathematics, Sookmyung Women's University, Seoul, Korea

Publication date: 2001-01-01