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).
Algebraic closure. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Algebraic_closure&oldid=32425