algebraic element over a field

代数元

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

Translation evidence: Literature usage

Meaning in context

An element α\alpha of an extension L/KL/K annihilated by a nonzero polynomial in K[x]K[x].

域扩张中能使基域上的某个非零多项式取值为零的元素。

Example

2\sqrt2 is algebraic over Q\mathbb Q.

Usage and distinctions

Algebraicity is relative to the base field; the zero polynomial cannot witness it.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author sourcedefinition def:algebraic-element, nonzero evaluation-kernel clause defining 代数元; specialize the ambient algebra to an extension field · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件definition def:algebraic-element, nonzero evaluation-kernel clause defining 代数元; specialize the ambient algebra to an extension field · Checked 2026-10-15
Edit source / propose a PRReport a correction

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