Algebraically closed field
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8/6/2026, 9:46:53 AM · Ancient Tree
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A [[Field|field]] $K$ is algebraically closed if every non-constant [[Polynomial|polynomial]] with coefficients in $K$ has at least one [[Root of a polynomial|root]] in $K$.2
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##### Examples4
- $\R$ is not algebraically closed, since the polynomial $P(X)=X^{2}+1$ has no root in $\R$.Revision 956
8/6/2026, 9:45:39 AM · Ancient Tree
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A field is algebraically closed if...1
A [[Field|field]] $K$ is algebraically closed if every non-constant [[Polynomial|polynomial]] with coefficients in $K$ has at least one [[Root of a polynomial|root]] in $K$.Revision 330
7/8/2026, 8:17:05 AM · Ancient Tree
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A field is algebraically closed if...