projective module

投射模

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Translation evidence: Literature usage

Meaning in context

A module $P$ such that every module map $P\to C$ lifts through every surjective module map $B\to C$.

到任意模的同态均能沿任意满同态提升的模。

Example

Every free module is projective.

Usage and distinctions

A projective module is a direct summand of a free module, but need not itself be free.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source投射模, 内射模, 平坦模, definition def:inj-proj-modules item 1; following paragraph 回到定义…它们的泛性质图解如下, item 1 gives the surjection-lifting criterion · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件投射模, 内射模, 平坦模, definition def:inj-proj-modules item 1; following paragraph 回到定义…它们的泛性质图解如下, item 1 gives the surjection-lifting criterion · Checked 2026-10-15

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