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
and an isomorphism
can be extended to an isomorphism
onto an algebraic extension
of the algebraic closure
The proof of the isomorphism extension theorem depends on Zorn's lemma.