View source for Algebraic closure

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''of a field $k$''

An algebraic extension (cf. [[Extension of a field|Extension of a field]]) of $k$ that is an [[Algebraically closed field|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|Algebra, fundamental theorem of]]).