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Algebraically closed field
Algebraic structure where all polynomials have roots
Algebraically closed field
In mathematics, a field F is algebraically closed if every non-constant polynomial with coefficients in F has a root in F. In other words, a field is algebraically closed if the fundamental theorem of algebra holds for it. For example, the field of real numbers is not algebraically closed because the polynomial x 2 + 1 {\displaystyle x^{2}+1} has no real roots, while the field of complex numbers is algebraically closed. Every field K {\displaystyle K} is contained in an algebraically closed field C , {\displaystyle C,} and the roots in C {\displaystyle C} of the polynomials with coefficients in K {\displaystyle K} form an algebraically closed field called an algebraic closure of...
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