Degree \(p\) extensions of an unramified regular local ring of mixed characteristic \(p\)
type: Item
instance of: scholarly article
title: Degree \(p\) extensions of an unramified regular local ring of mixed characteristic \(p\)
zbMATH Open document ID: 0602.13008
DOI: 10.1016/0021-8693(86)90029-3
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let \(R\) be an unramified regular local ring of mixed characteristic \(p\). The ``direct summand conjecture'', for module-finite extension rings of a regular Noetherian ring, can be reduced to the case of such a ring \(R\) [see \textit{M. Hochster}, J. Algebra 84, 503--553 (1983; Zbl 0562.13012)]. Let \(K\) be the fraction field of \(R\) and let \(u\in R\). It is shown that, for \(L=K(\root p\of{u})\) (and, also, for certain degree \(p^ 2\) extensions \(L\)), \(R\) is a direct summand of the integral closure of \(R\) in \(L\). A related example is given of a normal but non-Cohen-Macaulay ring.
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 3970880
zbMATH Keywords: unramified regular local ring
zbMATH Keywords: direct summand conjecture
zbMATH Keywords: direct summand of the integral closure
author: Jee Koh
reviewed by: C. P. L. Rhodes
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90029-3
OpenAlex ID: W2031162495
cites work: Contracted ideals from integral extensions of regular rings
cites work: Q4055756
cites work: Canonical elements in local cohomology modules and the direct summand conjecture
cites work: Splitting theorems for quadratic ring extensions
cites work: Abelian Extensions of Regular Local Rings
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description: scientific article; zbMATH DE number 3970880