finite field

有限域

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

Translation evidence: Literature usage

Meaning in context

A field with finitely many elements; its cardinality is pnp^n for a prime pp and positive integer nn.

元素个数有限的域，其元素个数必为素数的正整数次幂。

Example

F2[x]/(x2+x+1)\mathbb F_2[x]/(x^2+x+1) has four elements.

Usage and distinctions

A finite ring need not be a field; Z/4Z\mathbb Z/4\mathbb Z is not one.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source有限域, opening paragraph on positive characteristic and theorem prop:finite-field-uniqueness, |F|=p^[F:F_p] and positive extension degree · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件有限域, opening paragraph on positive characteristic and theorem prop:finite-field-uniqueness, |F|=p^[F:F_p] and positive extension degree · Checked 2026-10-15
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