Description: Ring of formal power series over a field $k$

Notes:

Keywords power series ring

Reference(s):

This ring has the following properties:

ACC principal
atomic domain
Bezout domain
Bezout ring
clean
coherent
connected
Dedekind domain
distributive
domain
GCD domain
Krull domain
local
Mori domain
Noetherian
normal
normal domain
principal ideal domain
principal ideal ring
Prufer domain
reduced
Schreier domain
semilocal
semiperfect
semiregular
serial
stable range 1
unique factorization domain
valuation

The ring lacks the following properties:

algebraically closed field
Artinian
characteristic 0 field
dual
Euclidean field
field
finite
Frobenius
Jacobson (Hilbert)
ordered field
perfect
perfect field
pseudo Frobenius
Pythagorean field
quadratically closed field
rad-nil
self-injective
semiprimary
semiprimitive
semisimple
strongly pi regular
von Neumann regular

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