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Separable extension

In field theory, a branch of algebra, an algebraic field extension E / F {\displaystyle E/F} is called a separable extension if for every α ∈ E {\displaystyle \alpha \in E} , the minimal polynomial of α {\displaystyle \alpha } over F is a separable polynomial (i.e., it is coprime to its formal derivative, or equivalently it has no repeated roots in any…

Separability of transcendental extensions, Overview & Separable and inseparable polynomials