annihilator of a module

模的零化子

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

Translation evidence: Literature usage

Meaning in context

For a module MM over a commutative ring RR, the ideal {r:rM=0}\{r:rM=0\}.

交换环中使模的每个元素都被乘成零的全部标量所组成的理想。

Example

Ann⁡Z(Z/6)=6Z\operatorname{Ann}_{\mathbb Z}(\mathbb Z/6)=6\mathbb Z.

Usage and distinctions

The annihilator of one vector may be larger than the annihilator of the entire module.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source模的基本操作 (sec:mod-operations), definition def:tor-ann, second item defining 模 M 的零化子 ann(M)={r:∀x∈M,rx=0} · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件模的基本操作 (sec:mod-operations), definition def:tor-ann, second item defining 模 M 的零化子 ann(M)={r:∀x∈M,rx=0} · Checked 2026-10-15
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