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.
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