On the weakly Arf (S2)-ifications of Noetherian rings
Abstract
The weakly Arf (S2)-ification of a commutative Noetherian ring R is considered to be a birational extension which is good next to the normalization. The weakly Arf property (WAP for short) of R was introduced in 1971 by J. Lipman with his famous paper [12], and recently rediscovered by [4], being closely explored with further developments. The present paper aims at constructing, for a given Noetherian ring R which satisfies certain mild conditions, the smallest module-finite birational extension of R which satisfies WAP and the condition (S2) of Serre. We shall call this extension the weakly Arf (S2)-ification, and develop the basic theory, including some existence theorems.
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