首页|Integrally Closed Ideals of Reduction Number Three
Integrally Closed Ideals of Reduction Number Three
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In a Cohen-Macaulay local ring(A,m),we study the Hilbert function of an integrally closed m-primary ideal I whose reduction number is three.With a mild assump-tion we give an inequality ℓA(A/I)≥ e0(I)-e1(I)+(e2(I)+ℓA(I2/QI))/2,where ei(I)denotes the ith Hilbert coefficient and Q denotes a minimal reduction of I.The inequality is located between inequalities of Itoh and Elias-Valla.Furthermore,this inequality be-comes an equality if and only if the depth of the associated graded ring of I is larger than or equal to dim A-1.We also study the Cohen-Macaulayness of the associated graded rings of determinantal rings.
Hilbert functionRees algebraassociated graded ringSally moduleCohen-Macaulay ring
Shinya Kumashiro
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National Institute of Technology(KOSEN),Oyama College 771 Nakakuki,Oyama,Tochigi,323-0806,Japan
JSPS KAKENHI Grant Number JP19J10579 and JP21K13766
NETL
NSTL
万方数据
维普
