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linearly disjoint
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(Definition)
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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.
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"linearly disjoint" is owned by CWoo.
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Cross-references: linearly independent, subset, field, subfields
There is 1 reference to this entry.
This is version 4 of linearly disjoint, born on 2004-04-21, modified 2004-04-22.
Object id is 5793, canonical name is LinearlyDisjoint.
Accessed 2310 times total.
Classification:
| AMS MSC: | 12F20 (Field theory and polynomials :: Field extensions :: Transcendental extensions) |
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Pending Errata and Addenda
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