Primary extension
In
purely inseparable over K.[1]
Properties
- An extension L/K is primary if and only if it is separable closure of K over K.[1]
- A subextension of a primary extension is primary.[1]
- A primary extension of a primary extension is primary (transitivity).[1]
- Any extension of a separably closed field is primary.[1]
- An extension is regular if and only if it is separable and primary.[1]
- A primary extension of a perfect field is regular.
References
- Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11 (3rd revised ed.). Zbl 1145.12001.
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