Isomorphism extension theorem

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 {displaystyle F} , an algebraic extension field {displaystyle E} of {displaystyle F} and an isomorphism {displaystyle phi } mapping {displaystyle F} onto a field {displaystyle F'} then {displaystyle phi } can be extended to an isomorphism {displaystyle tau } mapping {displaystyle E} onto an algebraic extension {displaystyle E'} of {displaystyle F'} (a subfield of the algebraic closure of {displaystyle F'} ).

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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