| dbo:abstract |
In algebra, a purely inseparable extension of fields is an extension k ⊆ K of fields of characteristic p > 0 such that every element of K is a root of an equation of the form xq = a, with q a power of p and a in k. Purely inseparable extensions are sometimes called radicial extensions, which should not be confused with the similar-sounding but more general notion of radical extensions. (en) Dans la théorie des extensions de corps, à l'opposé des extensions algébriques séparables, il existe les extensions radicielles. C'est un phénomène spécifique à la caractéristique positive et qui apparaît naturellement avec les corps de fonctions en caractéristique positive. (fr) 代数学において、体の純非分離拡大 (purely inseparable extension) は標数 p > 0 の体の拡大 k ⊆ K であって K のすべての元が q を p のベキ、a を k の元として xq = a の形の方程式の根であるようなものである。純非分離拡大はときどき radicial extension と呼ばれるが、名前の似たより一般的な概念である (radical extension) と混同してはならない。 (ja) |
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In algebra, a purely inseparable extension of fields is an extension k ⊆ K of fields of characteristic p > 0 such that every element of K is a root of an equation of the form xq = a, with q a power of p and a in k. Purely inseparable extensions are sometimes called radicial extensions, which should not be confused with the similar-sounding but more general notion of radical extensions. (en) Dans la théorie des extensions de corps, à l'opposé des extensions algébriques séparables, il existe les extensions radicielles. C'est un phénomène spécifique à la caractéristique positive et qui apparaît naturellement avec les corps de fonctions en caractéristique positive. (fr) 代数学において、体の純非分離拡大 (purely inseparable extension) は標数 p > 0 の体の拡大 k ⊆ K であって K のすべての元が q を p のベキ、a を k の元として xq = a の形の方程式の根であるようなものである。純非分離拡大はときどき radicial extension と呼ばれるが、名前の似たより一般的な概念である (radical extension) と混同してはならない。 (ja) |
| rdfs:label |
Extension radicielle (fr) 純非分離拡大 (ja) Purely inseparable extension (en) |
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freebase:Purely inseparable extension wikidata:Purely inseparable extension dbpedia-fr:Purely inseparable extension dbpedia-ja:Purely inseparable extension https://global.dbpedia.org/id/4tnym |
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