finitely generated module

有限生成模

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

Translation evidence: Literature usage

Meaning in context

An $R$-module spanned by a finite list of elements under finite $R$-linear combinations.

能由有限多个元素的环上线性组合生成的模。

Example

$\mathbb Z/6\mathbb Z$ is generated by $\bar1$.

Usage and distinctions

Finite generation does not imply that the underlying set is finite; $\mathbb Z$ is finitely generated.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source自由模 (sec:free-modules), definition immediately after prop:free-module-property, second item naming 有限生成模 through a finite generating set · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件自由模 (sec:free-modules), definition immediately after prop:free-module-property, second item naming 有限生成模 through a finite generating set · Checked 2026-10-15

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