Agnes Scott College

Judith D. Sally

Regular Overrings of Regular Local Rings
Transactions of the American Mathematical Society
Vol. 171, September 1972, pp291-300.


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.

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