View source for Isomorphism extension theorem

In [[Field theory (mathematics)|field theory]], a branch of [[Mathematics|mathematics]], the '''isomorphism extension theorem''' is an important [[Theorem|theorem]] regarding the extension of a [[Field (mathematics)|field]] [[Isomorphism|isomorphism]] to a larger field.
== Isomorphism extension theorem ==
The theorem states that given any field <math>F</math>, an algebraic extension field <math>E</math> of <math>F</math> and an isomorphism <math>\phi</math> mapping <math>F</math> onto a field <math>F'</math> then <math>\phi</math> can be extended to an isomorphism <math>\tau</math> mapping <math>E</math> onto an algebraic extension <math>E'</math> of <math>F'</math> (a subfield of the algebraic closure of <math>F'</math>).

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

==References==
* [[Biography:Donald John Lewis|D.J. Lewis]], ''Introduction to algebra'', Harper & Row, 1965, Chap.IV.12, p.193.

[[Category:Field (mathematics)]]
[[Category:Theorems in abstract algebra]]



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