Hilbert functions, reduction numbers and relation types

Yinghwa Wu, Purdue University

Abstract

Let (R,m) be a Cohen-Macaulay local ring having an infinite residue field and let I be an m-primary ideal. The reduction number, postulation number, and the relation type of I are studied when the depth of the associated graded ring of I is at least $d-2$, where $d\ge 2$ is the Krull dimension of R. By investigating the relationship between the postulation number and the reduction number of I (denoted by $r(I)$), conditions on I which force the independence of $r(I)$ are obtained. These results partially answer a question raised by J. Sally and generalize a previous result of Huckaba and Trung on the independence of the reduction number. In the last chapter we study the relation type of I, and give upper bounds for the relation type of I in terms of its reduction number and postulation number.

Degree

Ph.D.

Advisors

Heinzer, Purdue University.

Subject Area

Mathematics

COinS