Regular overrings of regular local rings
Author:
Judith Sally
Journal:
Trans. Amer. Math. Soc. 171 (1972), 291-300
MSC:
Primary 13H05
DOI:
https://doi.org/10.1090/S0002-9947-1972-0309929-3
Erratum:
Trans. Amer. Math. Soc. 213 (1975), 429.
MathSciNet review:
0309929
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Abstract | References | Similar Articles | Additional Information
Abstract: The local factorization theorem of Zariski and Abhyankar characterizes all -dimensional regular local rings which lie between a given
-dimensional regular local ring
and its quotient field as finite quadratic transforms of
. This paper shows that every regular local ring
of dimension
has infinitely many minimal regular local overrings which cannot be obtained by a monoidal transform of
. These overrings are localizations of rings generated over
by certain quotients of elements of an
-sequence. Necessary and sufficient conditions are given for this type of extension of
to be regular.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1972-0309929-3
Keywords:
Regular local ring,
overring,
valuation domain,
monoidal and quadratic transforms of a regular local ring,
dimension formula,
-sequence,
locality,
analytically irreducible domain
Article copyright:
© Copyright 1972
American Mathematical Society