A purely inseparable extension is an algebraic extension 
over a field 
if the algebraic
number minimal polynomial of any element has only one root, possibly with multiplicity.
Purely Inseparable Extension
See also
Extension Field, Field, Galois Theory, Perfect Field, Separable ExtensionThis entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Purely Inseparable Extension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PurelyInseparableExtension.html