ideal of a commutative ring

交换环的理想

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

Translation evidence: Literature usage

Meaning in context

An additive subgroup II of a commutative ring RR with rI⊆IrI\subseteq I for every r∈Rr\in R.

对环中任意元素的乘法均具有吸收性的加法子群。

Example

(2,x)(2,x) is an ideal of Z[x]\mathbb Z[x].

Usage and distinctions

An ideal need not contain 11; if it does, it equals the whole ring.

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Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source基本概念 (sec:ring-basics), definition def:ideals, additive-subgroup and scalar-absorption clauses, final commutative-ring convention · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件基本概念 (sec:ring-basics), definition def:ideals, additive-subgroup and scalar-absorption clauses, final commutative-ring convention · Checked 2026-10-15
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