identity element of a group

群的单位元

Algebra & Algebraic Geometry · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: neutral element · 幺元

Translation evidence: Literature usage

Meaning in context

The unique element $e$ of a group $G$ satisfying $eg=ge=g$ for all $g\in G$.

群中与任意元素在左右两侧运算都保持该元素不变的唯一元素。

Example

The identity in $\operatorname{GL}_2(\mathbb R)$ is $I_2$.

Usage and distinctions

The group identity is not a ring unit in the sense of an arbitrary invertible ring element.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. J. S. Milne — Group TheoryChapter 1, Definition 1.1, identity axiom · Checked 2026-10-14

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件半群, 幺半群与群，item naming 幺元或单位元 before def:monoid · Checked 2026-10-14

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