Separable extension

In the subfield of algebra named field theory, a separable extension is an algebraic field extension $E\supset F$ such that for every $\alpha\in E$ , the minimal polynomial of $\alpha$ over F is a separable polynomial (i.e., has distinct roots; see below for the definition in this context). Otherwise, the extension is called inseparable. There are other equivalent definitions of the notion of a separable algebraic extension, and these are outlined later in the article.

单词	Separable algebraic extension
释义	Separable algebraic extension 英语百科 Separable extension In the subfield of algebra named field theory, a separable extension is an algebraic field extension $E\supset F$ such that for every $\alpha\in E$ , the minimal polynomial of $\alpha$ over F is a separable polynomial (i.e., has distinct roots; see below for the definition in this context). Otherwise, the extension is called inseparable. There are other equivalent definitions of the notion of a separable algebraic extension, and these are outlined later in the article.
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Separable algebraic extension

Separable extension