algebraically closed

英語（米国） (en-US) 英語（イギリス） (en-GB)

形容詞

比較不可 前置詞句

(algebra, field theory, of a field) Which contains as an element every root of every nonconstant univariate polynomial definable over it (i.e., over said field).

日本語の意味

代数的に閉じた：ある体が、体上で定義可能な任意の非定数な一変数多項式のすべての根を自身の中に含む性質

英語の意味

(algebra, field theory, of a field) Which contains as an element every root of every nonconstant univariate polynomial definable over it (i.e., over said field).

このボタンはなに？

Working over an algebraically closed field often allows one to conclude that every polynomial equation has a solution within that field.

その上で定義されるすべての非定数一変数多項式の根を含む体の上で作業すると、多くの場合、任意の多項式方程式がその体内に解を持つと結論づけられます。

詳細

意味（1）

(algebra, field theory, of a field) Which contains as an element every root of every nonconstant univariate polynomial definable over it (i.e., over said field).

The fundamental theorem of algebra states that the field of complex numbers, ℂ, is algebraically closed.

詳細