Description: The integral closure of the integers in the complex numbers.

Notes: Krull dimension $1$.

Keywords integral closure

Reference(s):

This ring has the following properties:

The ring lacks the following properties:

ACC principal
algebraically closed field
Artinian
atomic domain
characteristic 0 field
Dedekind domain
dual
Euclidean domain
Euclidean field
field
finite
Frobenius
local
Noetherian
ordered field
perfect
perfect field
principal ideal domain
principal ideal ring
pseudo Frobenius
Pythagorean field
quadratically closed field
regular local
semilocal
semiperfect
semiprimary
semisimple
serial
unique factorization domain
valuation
von Neumann regular

We don't know if the ring has or lacks the following properties: