# Algebraic closure

From Encyclopedia of Mathematics

*of a field $k$*

An algebraic extension (cf. Extension of a field) of $k$ that is an algebraically closed field. Such an extension exists for each field and is unique up to isomorphism. The algebraic closure of the field of real numbers is the field of complex numbers (cf. Algebra, fundamental theorem of).

**How to Cite This Entry:**

Algebraic closure.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Algebraic_closure&oldid=32425

This article was adapted from an original article by V.N. Remeslennikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article