A uniformizer 
of a discrete valuation ring 
is an element such
that 
,
where 
is the unique maximal ideal
of 
. Equivalently, for the associated normalized
discrete valuation 
on the field of fractions
of 
, it satisfies 
(Milne 2020, pp. 46, 55-56).
Any two uniformizers differ by multiplication by a ring unit. Every nonzero element of 
can be written uniquely as 
, where 
is a ring unit and 
is a nonnegative integer
(Milne 2020, p. 46).
