unit of a ring

环的可逆元

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

Other names / variants: invertible element of a ring

Translation evidence: Literature usage

Meaning in context

An element uu in a unital ring admitting vv with uv=vu=1uv=vu=1.

在含幺环中具有双侧乘法逆元的元素。

Example

The units of Z\mathbb Z are 1,−11,-1.

Usage and distinctions

In a noncommutative ring, a one-sided inverse is not sufficient.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source几类特殊的环, paragraph beginning 既然 R 对乘法构成幺半群, R^× of 可逆元; two-sided inverse convention · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件几类特殊的环, paragraph beginning 既然 R 对乘法构成幺半群, R^× of 可逆元; two-sided inverse convention · Checked 2026-10-15
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