If a subset 
of the elements of a field 
satisfies the field axioms
with the same operations of 
,
then 
is called a subfield of 
. In a finite field of field
order 
,
with 
a prime, there exists a subfield of
field order 
for every 
dividing 
.
Subfield
See also
Extension Field, Field, Prime Subfield, Submanifold, SubspaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Subfield." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Subfield.html