Regular overrings of regular local rings

Sally, Judith

doi:10.1090/S0002-9947-1972-0309929-3

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: 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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