Regular overrings of regular local rings
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- by Judith Sally PDF
- Trans. Amer. Math. Soc. 171 (1972), 291-300 Request permission
Erratum: Trans. Amer. Math. Soc. 213 (1975), 429.
Abstract:
The local factorization theorem of Zariski and Abhyankar characterizes all $2$-dimensional regular local rings which lie between a given $2$-dimensional regular local ring $R$ and its quotient field as finite quadratic transforms of $R$. This paper shows that every regular local ring $R$ of dimension $n > 2$ has infinitely many minimal regular local overrings which cannot be obtained by a monoidal transform of $R$. These overrings are localizations of rings generated over $R$ by certain quotients of elements of an $R$-sequence. Necessary and sufficient conditions are given for this type of extension of $R$ to be regular.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 171 (1972), 291-300
- MSC: Primary 13H05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0309929-3
- MathSciNet review: 0309929