submodule

子模

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

Translation evidence: Literature usage

Meaning in context

An additive subgroup $N$ of an $R$-module $M$ closed under the $R$-scalar action.

模中对标量作用封闭的加法子群。

Example

$2\mathbb Z$ is a submodule of the $\mathbb Z$-module $\mathbb Z$.

Usage and distinctions

An arbitrary subgroup of the additive group need not be stable under other ring scalars.

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 def:submodule, additive-subgroup and scalar-closure clauses · 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 def:submodule, additive-subgroup and scalar-closure clauses · Checked 2026-10-15

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.