| 释义 |
algebraically closed (algebraic closure) A field is algebraically closed if every root of every polynomial with coefficients in the field is in the field. The Fundamental Theorem of Algebra shows that ℂ is algebraically closed. The algebraic closure of a field is the smallest extension of the field which is algebraically closed. So, the algebraic closure of R is ℂ and the algebraic closure of ℚ is the field of algebraic numbers.
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