Let 
be a number field of extension
degree 
over 
.
Then an order 
of 
is a subring of the ring of integers of 
with 
generators over 
, including 1.
The ring of integers of every number field 
is an order, known as the maximal
order, of 
.
Every order of 
is contained in the maximal order. If 
is an algebraic integer
in 
,
then ![Z[alpha]](/images/equations/NumberFieldOrder/Inline14.svg)
is an order of 
,
though it may not be maximal if 
is greater than 2.
