Isomorphism extension theorem

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In field theory, a branch of mathematics, the isomorphism extension theorem is an important theorem regarding the extension of a field isomorphism to a larger field.

[edit] Isomorphism extension theorem

The theorem states that given any field F and its algebraic extension field E and an isomorphism φ mapping F onto a field F' then φ can be enlarged to an isomorphism τ mapping E onto a subfield of which is the algebraic closure of F' and τ(a) = φ(a) for all .

The proof of the isomorphism extension theorem depends on Zorn's lemma.