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primary extension
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''.〔Fried & Jarden (2008) p.44〕
==Properties==
* An extension ''L''/''K'' is primary if and only if it is linearly disjoint from the separable closure of ''K'' over ''K''.〔
* A subextension of a primary extension is primary.〔
* A primary extension of a primary extension is primary (transitivity).〔
* Any extension of a separably closed field is primary.〔
* An extension is regular if and only if it is separable and primary.〔
* A primary extension of a perfect field is regular.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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