quotient module

商模

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

Translation evidence: Literature usage

Meaning in context

For a submodule N≤MN\le M, the additive quotient M/NM/N with scalar action r(m+N)=rm+Nr(m+N)=rm+N.

由子模取加法商并以代表元标量运算诱导作用所得的模。

Example

Z/3Z\mathbb Z/3\mathbb Z is the quotient of Z\mathbb Z by 3Z3\mathbb Z.

Usage and distinctions

Scalar stability of NN is needed for the action to be well-defined.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source基本概念, definition naming 商模, (m+N)+(m′+N) and r(m+N)=rm+N · 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, definition naming 商模, (m+N)+(m′+N) and r(m+N)=rm+N · Checked 2026-10-15
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