left module

左模

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

Translation evidence: Literature usage

Meaning in context

An abelian group with a distributive, associative unital left scalar action of a ring RR.

带有含幺环的左标量作用且满足分配律、结合律和单位律的交换群。

Example

Any abelian group becomes a Z\mathbb Z-module.

Usage and distinctions

For noncommutative rings left and right actions cannot be interchanged without further structure.

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Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source基本概念, first definition of 左 R-模, abelian additive group and four unital scalar-action axioms · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件基本概念, first definition of 左 R-模, abelian additive group and four unital scalar-action axioms · Checked 2026-10-15
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