Description: The ring is the (semi)localization of the integers at the multiplicative set of numbers not divisible by either of $2$ and $3$

Notes: Exactly two maximal ideals. Krull dimension $1$.

Keywords localization

Reference(s):

- , None Needed, , (1). N/A

This ring has the following properties:

ACC principal
atomic domain
Bezout domain
Bezout ring
Cohen-Macaulay
coherent
connected
Dedekind domain
distributive
domain
GCD domain
Gorenstein
Krull domain
Mori domain
Noetherian
normal
normal domain
principal ideal domain
principal ideal ring
Prufer domain
reduced
regular
Schreier domain
semilocal
stable range 1
unique factorization domain

The ring lacks the following properties:

algebraically closed field
Artinian
characteristic 0 field
clean
continuous
dual
Euclidean field
field
finite
Frobenius
Kasch
local
ordered field
perfect
perfect field
pseudo Frobenius
Pythagorean field
quadratically closed field
regular local
self-injective
semiperfect
semiprimary
semiregular
semisimple
serial
strongly pi regular
valuation
von Neumann regular

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