Isomorphism extension theorem

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

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

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

References

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