algebraically closed field oor Tsjeggies
algebraically closed field
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field in which every polynomial is factorizable into monomials
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A field with no nontrivial algebraic extensions is called algebraically closed.
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Algebraically closed field - Wikipedia
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The theory of algebraically closed fields has quantifier elimination.
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Algebraically closed field
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The same argument proves that no subfield of the real field is algebraically closed; in particular, the field of rational numbers is not algebraically closed.
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The completion of this algebraic closure, however, is algebraically closed. Because of its rough analogy to the complex numbers, it is called the field of complex p-adic numbers and is denoted by Cp.[39]
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