A valuation theorem for Noetherian rings
Commutative Algebra
2021-10-27 v2 Algebraic Geometry
Abstract
Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A' the integral closure of A in B. We show that A' is determined by finitely many unique discrete valuation rings. Our result generalizes Rees' classical valuation theorem for ideals. We also obtain a variant of Zariski's main theorem.
Cite
@article{arxiv.2011.14749,
title = {A valuation theorem for Noetherian rings},
author = {Antoni Rangachev},
journal= {arXiv preprint arXiv:2011.14749},
year = {2021}
}
Comments
Accepted in the Michigan Mathematical Journal. The current version has 7 pages, incorporates the referee's comments, and has an improved exposition