Harman Patil (Editor)

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.

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.

    • References

    Primary extension Wikipedia
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