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separable field extension

Contents

Definition

A polynomial PP over a field KK is separable if all its irreducible factors have distinct roots over the algebraic closure K¯\bar{K} of KK.

An extension KLK\subset L of fields is separable if every element xLx\in L is a root of a separable polynomial over KK.

Properties

Every finite separable field extension is an étale morphism of rings.

If KLMK\subset L\subset M are fields and KMK\subset M is separable, then LML\subset M is also separable.

Revised on December 9, 2013 05:55:15 by Urs Schreiber (89.204.139.250)