Last Updated
：2025/11/28
algebraic closure
Noun
of a field F
Japanese Meaning
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。
（ plural ）
Quizzes for review
(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).
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algebraic closure
During the seminar, she explained why the algebraic closure of the rational numbers is fundamental to understanding polynomial roots.
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During the seminar, she explained why the algebraic closure of the rational numbers is fundamental to understanding polynomial roots.
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