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

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

• D.J. Lewis, Introduction to algebra, Harper & Row, 1965, Chap.IV.12, p.193.