flat module

平坦模

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

Translation evidence: Literature usage

Meaning in context

A module over a commutative ring for which tensoring preserves every short exact sequence.

在交换环上，与之张量的函子保持所有短正合列的模。

Example

Q\mathbb Q is flat over Z\mathbb Z.

Usage and distinctions

Flatness requires exact tensoring, not finite generation or existence of a basis.

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, unnamed definition of 平坦模 immediately after def:inj-proj-modules, exact tensor functor; commutative-ring specialization · 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, unnamed definition of 平坦模 immediately after def:inj-proj-modules, exact tensor functor; commutative-ring specialization · Checked 2026-10-15
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