free module

自由模

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Translation evidence: Literature usage

Meaning in context

An RR-module with a basis, equivalently a direct sum of copies of RR indexed by a set.

具有基、等价地同构于若干个环自身之直和的模。

Example

R3R^3 is free with its coordinate basis.

Usage and distinctions

Finitely generated modules need not be free; Z/2Z\mathbb Z/2\mathbb Z is not free over Z\mathbb Z.

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Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source自由模 (sec:free-modules), definition def:free-module and intrinsic basis definition immediately after prop:free-module-property · 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 def:free-module and intrinsic basis definition immediately after prop:free-module-property · Checked 2026-10-15
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