Note on ideal-transforms, Rees rings, and Krull rings
type: Item
instance of: scholarly article
title: Note on ideal-transforms, Rees rings, and Krull rings
zbMATH Open document ID: 0631.13003
DOI: 10.1016/0021-8693(87)90053-6
author: Paul M. jun. Eakin
author: Daniel Katz
author: William J. Heinzer
author: Louis J. Ratliff
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The main result gives several necessary and sufficient conditions for the ideal transform T(I) to be finitely generated over R, when I is a height one ideal in an important class of two-dimensional local rings R. One of these conditions is that the integral closure of T(I) coincides with the complete integral closure of T(I). Then it is shown that if I is an ideal in a Noetherian ring and I contains a regular element, then the complete integral closure of T(I) is always a Krull ring. This is applied to certain symbolic Rees rings.
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 4025554
zbMATH Keywords: ideal transform
zbMATH Keywords: complete integral closure
zbMATH Keywords: Krull ring
zbMATH Keywords: symbolic Rees rings
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90053-6
OpenAlex ID: W2034118583
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description: scientific article; zbMATH DE number 4025554