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Summary Of: Algebraically closed

Another example of an algebraically closed field is the field of... is algebraically closed if and only if the only... is algebraically closed if and only if every polynomial... is algebraically closed follows from the previous property together with the fact that... is algebraically closed if and only if it has no proper... is algebraically closed if and only if it has no finite... is algebraically closed if and only if... is algebraically closed if and only if every... Thus algebraically closed fields are cyclotomically closed... then it is true for every algebraically closed field with the same... if such a proposition is valid for an algebraically closed field with characteristic... not only is it valid for all other algebraically closed fields with characteristic... such that the proposition is valid for every algebraically closed field with characteristic...

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mathematics | field | polynomial | variable | coefficients | root | real numbers | rational numbers | finite field | fundamental theorem of algebra | complex numbers | algebraic numbers | irreducible polynomials | ring | coefficients | splits into linear factors | algebraic extension | quotient | ideal | degree | minimal polynomial | algebraic extension | previous proof | linear map | eigenvector | characteristic polynomial | companion matrix | rational function | theorem on partial fraction decomposition | first-order logic | characteristic | up to isomorphism | algebraic extension | algebraic closure | Barwise, Jon | ISBN 0-7204-2285-X | Lang, Serge | ISBN 0-387-95385-X | van der Waerden, Bartel Leendert | ISBN 0-387-40624-7 | Categories | Abstract algebra | Field theory |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Algebraically closed".