Every algebraic extension of a field of characteristic zero is separable, and every algebraic extension of a finite field is separable. Separable and inseparable... · Separable elements and...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots.

An irreducible polynomial P over F is separable if and only if P has pairwise distinct roots in an algebraic closure of F.

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Опубликовано: 1 янв. 2021 г.

In mathematics, more specifically in the area of modern algebra known as field theory, an algebraic extension is a separable extension if and only if for ...

4 нояб. 2019 г. · An extension K/F is separable iff every element of K has a separable minimal polynomial over F. Minimal polynomials are irreducible, ... galois theory - The definition of the separable closure of a field Every finite extension of a finite field is separable tower of separable extension - Math Stack Exchange galois theory - Compositum of separable extension Другие результаты с сайта math.stackexchange.com

In this section we talk about separability for nonalgebraic field extensions. This is closely related to the concept of geometrically reduced algebras.

A finite extension L/K is called separable if every element of L is separable over K. When L/K is not separable, it is called inseparable. Example 3.2 ...

(algebra) A finite (and thereby algebraic) extension of a base field such that every element of the extension is the root of a separable polynomial over the ...

31 авг. 2024 г. · A field F is called perfect if all irreducible polynomials over F are separable, and as a consequence every algebraic extension of F is ...