Euclidean Rings of Algebraic Integers

[摘要] Let $K$ be a finite Galois extension of the field of rational numberswith unit rank greater than~3. We prove that the ring of integers of$K$ is a Euclidean domain if and only if it is a principal idealdomain. This was previously known under the assumption of thegeneralized Riemann hypothesis for Dedekind zeta functions. We nowprove this unconditionally.

[学科分类] 数学（综合）