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.

The theorem states that given any field F , an algebraic extension field E of F and an isomorphism ϕ mapping F onto a field F ′ then ϕ can be extended to an isomorphism τ 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.

References

Isomorphism extension theorem Wikipedia

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