On the weakly Arf $(S_2)$-ifications of Noetherian rings
Commutative Algebra
2022-04-27 v1
Abstract
The weakly Arf -ification of a commutative Noetherian ring is considered to be a birational extension which is good next to the normalization. The weakly Arf property (WAP for short) of 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 which satisfies certain mild conditions, the smallest module-finite birational extension of which satisfies WAP and the condition of Serre. We shall call this extension the weakly Arf -ification, and develop the basic theory, including some existence theorems.
Keywords
Cite
@article{arxiv.2204.12132,
title = {On the weakly Arf $(S_2)$-ifications of Noetherian rings},
author = {Naoki Endo and Shiro Goto and Shin-ichiro Iai and Naoyuki Matsuoka},
journal= {arXiv preprint arXiv:2204.12132},
year = {2022}
}