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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of the Auslander-Nagata
purity theorem


Author: Miriam Ruth Kantorovitz
Journal: Proc. Amer. Math. Soc. 127 (1999), 71-78
MSC (1991): Primary 13B15; Secondary 13B02
DOI: https://doi.org/10.1090/S0002-9939-99-04501-3
MathSciNet review: 1458881
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Abstract: Let $B \hookrightarrow A$ be a module finite extension of normal domains. We show that if $B \hookrightarrow A$ is unramified in codimension one and if $A$ has finite projective dimension over $B$, then $A$ is étale over $B$. Our proof makes use of P. Roberts' New Intersection Theorem.


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Additional Information

Miriam Ruth Kantorovitz
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: ruth@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04501-3
Keywords: Auslander-Nagata purity, unramified extension
Received by editor(s): October 17, 1996
Received by editor(s) in revised form: May 14, 1997
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society