# separably algebraically closed field

A field $K$ is called *separably algebraically closed* if every separable element of the algebraic closure^{} of $K$ belongs to $K$.

In the case when $K$ has characteristic^{} 0, it is separably algebraically closed if and only if it is algebraically closed.

If $K$ has positive characteristic $p$, $K$ is separably algebraically closed if and only if its algebraic closure is a purely inseparable extension of $K$.

Title | separably algebraically closed field |
---|---|

Canonical name | SeparablyAlgebraicallyClosedField |

Date of creation | 2013-03-22 15:58:30 |

Last modified on | 2013-03-22 15:58:30 |

Owner | polarbear (3475) |

Last modified by | polarbear (3475) |

Numerical id | 6 |

Author | polarbear (3475) |

Entry type | Definition |

Classification | msc 12F05 |

Defines | separably algebraically closed |