A discrete valuation ring is a local ring that is a principal ideal domain and is not a field
(Milne 2020, p. 46). Its unique nonzero prime ideal is generated by a uniformizer 
, and every nonzero element is a ring unit times
a power 
, where 
is a nonnegative integer.
The quotient ring by 
is its residue field.
Completeness refers to the topology defined by the powers 
.
For a perfect field 
of positive field
characteristic 
, the ring 
of 
-typical Witt vectors is a complete
discrete valuation ring with uniformizer 
(Milne 2017, p. 228). The integral form of Donovan's
conjecture fixes such a coefficient ring
before counting Morita equivalence classes
(Eaton et al. 2020).
