If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, with p a prime, there exists a subfield of field order p^m for every m dividing n.

See also

Extension Field, Field, Prime Subfield, Submanifold, Subspace

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Cite this as:

Weisstein, Eric W. "Subfield." From MathWorld--A Wolfram Web Resource.

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