field

域

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

Translation evidence: Literature usage

Meaning in context

A commutative unital ring with $1\ne0$ in which every nonzero element is a unit.

满足 $1\ne0$ 且每个非零元素都可逆的交换含幺环。

Example

$\mathbb Z/5\mathbb Z$ is a field.

Usage and distinctions

A division ring need not be commutative; field means commutative here.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source几类特殊的环, definition def:field, 域 as a commutative division ring, under the section's nonzero-ring convention · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件几类特殊的环, definition def:field, 域 as a commutative division ring, under the section's nonzero-ring convention · Checked 2026-10-15

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