# linearly disjoint

Let $E$ and $F$ be subfields^{} of $L$, each containing a field $K$. $E$ is said to be *linearly disjoint* from $F$ over $K$ if every subset of $E$ linearly independent^{} over $K$ is also linearly independent over $F$.

Remark. If $E$ is linearly disjoint from $F$ over $K$, then $F$ is linearly disjoint from $E$ over $K$. Then one can speak of $E$ and $F$ being linearly disjoint over $K$ without causing any confusions.

Title | linearly disjoint |
---|---|

Canonical name | LinearlyDisjoint |

Date of creation | 2013-03-22 14:19:28 |

Last modified on | 2013-03-22 14:19:28 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 7 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 12F20 |