Let 
be a non-Archimedean field. Its valuation
ring 
is defined to be
 |
The valuation ring has maximal ideal
 |
and the field 
is called the residue field, class field, or field of digits.
For example, if 
(p-adic numbers), then 
(
-adic integers), 
(
-adic integers congruent to 0 mod 
), and 
= GF(
), the finite field of order
.
