Krull–Akizuki theorem
id:
krull-akizuki-theorem-194-508428
title:
Krull–Akizuki theorem
text:
In commutative algebra, the Krull–Akizuki theorem states the following: Let A be a one-dimensional reduced noetherian ring, K its total ring of fractions. Suppose L is a finite extension of K. If A ⊂ B ⊂ L and B is reduced,
then B is a one-dimensional noetherian ring. Furthermore, for every nonzero ideal I of B, B / I is finite over A. Note that the theorem does not say that B is finite over A. The theorem does not extend to higher dimension. One important consequence of the theorem is that the
brand slug:
wiki
category slug:
encyclopedia
description:
About extensions of one-dimensional Noetherian rings (commutative algebra)
original url:
https://en.wikipedia.org/wiki/Krull%E2%80%93Akizuki_theorem
date created:
date modified:
2023-10-08T17:36:31Z
main entity:
{"identifier":"Q6439289","url":"https://www.wikidata.org/entity/Q6439289"}
image:
fields total:
13
integrity:
14