chain complex of modules

模的链复形

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

Translation evidence: Literature usage

Meaning in context

Modules $C_n$ and maps $d_n:C_n\to C_{n-1}$ with $d_{n-1}d_n=0$ for every integer $n$ .

配备降一次指标的模同态且相邻两个微分复合为零的模族。

$\mathbb Z\xrightarrow{2}\mathbb Z$ in degrees one and zero is a chain complex.

A complex need not be exact; cochain conventions instead raise the index.

Wen-Wei Li — Methods in Algebra II, author sourceremark rem:cochain-vs-chain (链复形的同调), decreasing-index complex and d_{n-1}d_n=0; specialize to modules · Checked 2026-10-15

李文威 — 代数学方法卷二，作者源文件remark rem:cochain-vs-chain (链复形的同调), explicit naming of decreasing-index 链复形 versus increasing-index 上链复形 · Checked 2026-10-15

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