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created: 2021-11-05 23:49:34
modified: 2022-01-19 16:18:10
Let be a polynomial with coefficients in a field .
We say that is a root of if
The field is algebraically closed if every polynomial with coefficients in has a root .
Examples
- The field is not algebraically closed because has coefficients in but there is no real number root of it
- The field of complex numbers is algebraically closed (due to the fundamental theorem of algebra)