English Dictionary

algebraic closure

名詞

前置詞句

(algebra, field theory, of a field F) A field G such that every polynomial over F splits completely over G (i.e., every element of G is a root of some polynomial over F and every root of every polynomial over F is an element of G).

日本語の意味

代数的閉包: ある体 F に対して、F 上のすべての多項式が完全に因数分解されるような体 G を指す。すなわち、G の各要素は F 上の何らかの多項式の根となり、F 上の全ての多項式の全ての根が G の要素である。

During the seminar, she explained why the algebraic closure of the rational numbers is fundamental to understanding polynomial roots.

セミナーで、彼女は有理数の代数的閉包が多項式の根を理解するうえでなぜ基本的なのかを説明した。

意味（1）

(algebra, field theory, of a field F) A field G such that every polynomial over F splits completely over G (i.e., every element of G is a root of some polynomial over F and every root of every polynomial over F is an element of G).

The calculation of these various Galois groups leads to a determination of the algebraic closures of the ground fields in the splitting fields of the corresponding vectorial polynomials.

algebraic closures （ plural ）