# 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 LinearlyDisjoint 2013-03-22 14:19:28 2013-03-22 14:19:28 CWoo (3771) CWoo (3771) 7 CWoo (3771) Definition msc 12F20