trivial absolute value

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(number theory) An absolute value (or norm) for a field which is defined to be equal to one for any element of the field other than the field's zero, for which it is defined to be equal to zero.

日本語の意味

数論において、体の非零の任意の元に対して1、零には0と定義される絶対値（またはノルム）のこと。

英語の意味

(number theory) An absolute value (or norm) for a field which is defined to be equal to one for any element of the field other than the field's zero, for which it is defined to be equal to zero.

このボタンはなに？

The trivial absolute value on a number field assigns 1 to every nonzero element and 0 to zero, so it conveys no information about valuations.

体上の自明な絶対値は、すべての非零元に1を、零元に0を割り当てるため、付値に関する情報を一切提供しません。

詳細

意味（1）

(number theory) An absolute value (or norm) for a field which is defined to be equal to one for any element of the field other than the field's zero, for which it is defined to be equal to zero.

The trivial absolute value gives rise to the discrete metric.

詳細

trivial absolute values （ plural ）