unital ring

含幺环

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

Translation evidence: Literature usage

Meaning in context

An abelian additive group with associative multiplication, two-sided distributivity, and a multiplicative identity.

加法构成交换群、乘法结合并对加法满足双侧分配律且有乘法单位元的集合。

Example

M2(R)M_2(\mathbb R) is a noncommutative unital ring.

Usage and distinctions

Commutativity of multiplication is an extra assumption; ring maps here preserve identity.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source环的定义, first definition: additive group, associative multiplication, distributive and identity clauses · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件基本概念 (sec:ring-basics), first definition beginning (含幺)环, multiplicative identity clause and contrast with 无幺环 · Checked 2026-10-15
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