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.