The ring of integers of a number field 
,
denoted 
,
is the set of algebraic integers in 
, which is a ring of dimension 
over 
, where 
is the extension degree
of 
over 
. 
is also sometimes called the maximal order of 
.
Maximal Order
See also
Algebraic Integer, Extension Field Degree, Number Field, Number Field Order, Ring, Ring of IntegersPortions of this entry contributed by David Terr
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Cite this as:
Terr, David and Weisstein, Eric W. "Maximal Order." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MaximalOrder.html