Birational extensions of regular local rings and local UFDs
type: Item
instance of: scholarly article
title: Birational extensions of regular local rings and local UFDs
zbMATH Open document ID: 0704.13012
DOI: 10.1016/0021-8693(90)90075-Y
author: Bernard L. Johnston
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: This paper is a contribution to the problem of investigation of birational extensions of regular local rings in dimension bigger or equal to three. We recall the following results of Abhyankar-Zariski: if \(R\subset S\) are regular local rings of dimension two with the same quotient field then S can be obtained from R by a finite sequence of quadratic transformations. The same problem in dimension three or more is much more complicated, here we can find some partial results and a new point of view to study this problem based in the ``irregular locus'' of an extension. A good account on this problem can be found in the paper by \textit{J. Lipman} in Algebraic geometry and commutative algebra, Pap. in Honor of Masayoshi Nagata, Vol. I, 203-231 (1988; Zbl 0693.13011).
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 13F15
zbMATH DE Number: 4154591
zbMATH Keywords: UFD
zbMATH Keywords: birational extensions of regular local rings
zbMATH Keywords: irregular locus
reviewed by: Marcel Morales
MaRDI profile type: Publication
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full work available at URL: 0021-8693(90)90075-y
OpenAlex ID: W2042541468
description: scientific article; zbMATH DE number 4154591