Primary extension
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In field theory, a branch of algebra, a primary extension L of K is a field extension such that the algebraic closure of K in L is purely inseparable over K.[1]
Properties
[edit | edit source]- An extension L/K is primary if and only if it is linearly disjoint from the 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
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