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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
.
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.
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.
