monoid

幺半群

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

Translation evidence: Literature usage

Meaning in context

A set with an associative binary operation and a two-sided identity element.

具有结合的二元运算及双侧单位元的集合。

Example

(Z≥0,+)(\mathbb Z_{\ge0},+) is a monoid with identity 00.

Usage and distinctions

A monoid need not have inverses; its invertible elements form a group.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source半群, 幺半群与群，definition labelled def:monoid, associativity and identity clauses · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件半群, 幺半群与群，definition heading 半群与幺半群; index entry 幺半群 (monoid) · Checked 2026-10-14
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