Translation guide
In mathematics, an identity element is a special element in a set that leaves other elements unchanged when combined with them. This guide covers how to express this concept in Japanese.
The element in a set that, when combined with any other element via a binary operation, leaves that element unchanged.
Standard term for identity element in abstract algebra. Used for groups, rings, etc.
群の単位元は一意に定まる。
The identity element of a group is uniquely determined.
Less common synonym for identity element, sometimes used in older texts.
この演算の恒等元は0である。
The identity element for this operation is 0.
Phrase meaning 'is the identity element'. Used in definitions.
eはこの群の単位元である。
e is the identity element of this group.
Specifically the additive identity (0 in many structures).
実数における加法単位元は0です。
The additive identity in real numbers is 0.
Specifically the multiplicative identity (1 in many structures).
乗法単位元は1であることが多い。
The multiplicative identity is often 1.
In mathematics, always use 単位元 for the general concept. For specific operations, you can say 加法単位元 (additive identity) or 乗法単位元 (multiplicative identity).