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.

Isomorphism extension theorem[edit]

The theorem states that given any field F, an algebraic extension field E of F and an isomorphism \phi mapping F onto a field F' then \phi can be extended to an isomorphism \tau mapping E onto an algebraic extension E' of F' (a subfield of the algebraic closure of F').

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