Hilbert coefficients and Buchsbaumness of associated graded rings

By S. Goto, Koji Nishida. 2003

49 citations recorded by the source corpus.

Let A be a Noetherian local ring with the maximal ideal m and I an m-primary ideal. The purpose of this paper is to generalize Northcott's inequality on Hilbert coefficients of I given in Northcott (J. London Math. Soc. 35 (1960) 209), without assuming that A is a Cohen–Macaulay ring. We will investigate when our inequality turns into an equality. It is related to the Buchsbaumness of the associated graded ring of I.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/576af1e3c4a815081d82921f356bce2d4adf21a1

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Hilbert Functions of Filtered Modules (2007, methodology): “Notice that it does not imply that grq(A) is Cohen-Macaulay, nor even that grq(A) is Buchsbaum (see [31], Theorem 3.”