Last Updated：2025/12/04

Dictionary quizzes to help you remember vocabulary

Dictionary quizzes to help you remember vocabulary

(algebra, ring theory) The smallest field in which a given ring can be embedded.

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field of fractions

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Source Word

field of fractions

(algebra, ring theory) The smallest field in which a given ring can be embedded.

Japanese Meaning

与えられた環が埋め込まれる最小の体。数学（特に代数学・環論）において、環を体に拡大するための最小の構造。

What is this buttons?

To solve this problem, we extend the integral domain to its field of fractions.

Google Translation / DeepL Translation

この問題を解くために、整域をその分数体に拡張する。

Sense（1）

(algebra, ring theory) The smallest field in which a given ring can be embedded.

The general construction of the field of fractions ℚ_R out of R is an exact parallel of the construction of the field of rational numbers ℚ out of the ring of integers ℤ.

Google Translation / DeepL Translation

fields of fractions

（ plural ）

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