separable algebraic extension
可分扩张
Meaning in context
An algebraic extension in which every element's minimal polynomial has distinct roots in an algebraic closure.
每个元素在基域上的极小多项式均无重根的代数扩张。
Example
Every algebraic extension in characteristic zero is separable.
Usage and distinctions
An algebraic extension in positive characteristic need not be separable.
Recommended reading in this subject · Preparation & skip guidance
Definition sources
- Wen-Wei Li — Methods in Algebra I, author source可分性, definition headed 可分元 (minimal polynomial without repeated roots), and later definition naming an algebraic 可分扩张 when every element is separable · Checked 2026-10-15
Translation sources
- 李文威 — 代数学方法 卷一，作者源文件可分性, definition headed 可分元 (minimal polynomial without repeated roots), and later definition naming an algebraic 可分扩张 when every element is separable · Checked 2026-10-15