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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…

Equivalent properties, Overview & Examples