Depth of Rees algebra and associated graded rings and integrally closed ideals in two-dimensional regular local rings

Mee-Kyoung Kim, Purdue University

Abstract

This thesis contains two different strains of commutative algebra. These are joined together to form the title of the thesis. Depth of Rees algebra and associated graded rings. Let (R, m) be a Cohen-Macaulaylocal ring and I be an ideal with positive height. We obtain a relation between the depth of $R\lbrack It\rbrack$ and the depth of $gr\sb{I}(R).$ We do this by studying equimultiple ideals I and the condition that R is normally Cohen-Macaulay along I. Integrally closed ideals in 2-dimensional regular local rings. Let (R, m, k) be a 2-dimensional regular local ring with algebraically closed residue field k and with quotient field K, and let I be an m-primary integrally closed ideal in R. By Zariski's Unique Factorization Theorem, $I = I\sbsp{1}{\mu\sb1}\... I\sbsp{\ell}{\mu\sb\ell},$ where $I\sb1,\...,I\sb\ell$ are distinct simple m-primary integrally closed ideals of R. We study an m-primary integrally closed ideal I in R such that $I=I\sb1\... I\sb\ell,$ where $I\sb1,\...,I\sb\ell$ are distinct simple m-primary integrally closed ideals in R.

Degree

Ph.D.

Advisors

Heinzer, Purdue University.

Subject Area

Mathematics

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