Last Updated：2025/11/28

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(algebra, field theory) A field L which contains a subfield K, called the base field, from which it is generated by adjoining extra elements.

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extension field

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Source Word

extension field

Noun

Japanese Meaning

（代数学、体論）ある部分体K（基底体）を包含し、そのKに対して追加の元を隣接（拡張）することで構成される体。

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The extension field L over K is constructed by adjoining to K all the roots of a given polynomial.

Google Translation / DeepL Translation

拡大体Lは、与えられた多項式のすべての根を基底体Kに加えることで構成される。

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Sense（1）

Suppose F is a subfield of the field K. Then K is called an extension field of F. So, for instance, GF(4) and GF(8) are extension fields of GF(2), although GF(8) is not an extension field of GF(4).

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extension fields

（ plural ）

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extension field

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