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In field theory, a simple extension is a field extension that is generated by the adjunction of a single element, called a primitive element. Simple extensions are well understood and can be completely classified.
Definition, Structure of simple extensions & Examples
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Simple extension | is a | field extension that is generated by the adjunction of a single element | 0.90 | text |
| the rationals | instance of | For a field of characteristic 0 | 0.80 | text |
| this means all finite extensions are simple | instance of | For a field of characteristic 0 | 0.80 | text |
| Simple extension | related to Definition | L/K | 0.60 | section |
| Simple extension | related to Definition | This | 0.60 | section |
| Simple extension | related to Definition | Equivalently | 0.60 | section |
| Simple extension | related to Examples | Any | 0.60 | section |
| Simple extension | related to Examples | For | 0.60 | section |
| Simple extension | related to Structure of simple extensions | Let | 0.60 | section |
| Simple extension | related to Structure of simple extensions | For | 0.60 | section |
| Simple extension | related to Structure of simple extensions | Two | 0.60 | section |
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