Separate conclusion

Separable degree is a term used in algebra .

If there is a separable algebraic field extension , then the following statements are equivalent: ${\displaystyle L/K}$

• Every non-constant separable polynomial in is completely broken down into linear factors. ${\displaystyle L[X]}$
• If an algebraic closure of and is embedded in , then the extension is purely inseparable . ${\displaystyle C}$ ${\displaystyle K}$ ${\displaystyle L}$ ${\displaystyle C}$ ${\displaystyle C/L}$

For every body there is a clearly defined body with the above properties, except for isomorphism . It is also referred to as and is called the separable algebraic closure of . ${\displaystyle K}$ ${\displaystyle L}$ ${\displaystyle K_{\rm {sep}}}$ ${\displaystyle K}$