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Northcott type inequality for Buchsbaum-Rim coefficients
Published in Rocky Mountain Mathematics Consortium
2016
Volume: 8
   
Issue: 4
Pages: 493 - 512
Abstract
In 1960, Northcott [13] proved that, if e0(I) and e1(I) denote the 0th and first Hilbert-Samuel coefficients of an m-primary ideal I in a Cohen-Macaulay local ring (R,m), then e0(I) - e1(I) ≤ l(R/I). In this article, we study an analogue of this inequality for Buchsbaum-Rim coefficients. We prove that, if (R,m) is a two dimensional Cohen-Macaulay local ring and M is a finitely generated Rmodule contained in a free module F with finite co-length, then br0(M)-br1(M) ≤ l(F/M), where br0(M) and br1(M) denote 0th and 1st Buchsbaum-Rim coefficients, respectively. © 2016 Rocky Mountain Mathematics Consortium.
About the journal
JournalJournal of Commutative Algebra
PublisherRocky Mountain Mathematics Consortium
ISSN19390807
Open AccessYes