An inseparable extension is an algebraic field extension which is not separable. Thus some element
has a minimal polynomial with a repeated root in an algebraic closure. Inseparable
extensions can occur only in positive field characteristic;
for example, adjoining a 
th root of 
to the rational function field 
gives an inseparable extension.
Inseparable Extension
See also
Algebraic Extension, Field Characteristic, Perfect Field, Separable ExtensionExplore with Wolfram|Alpha
References
Dummit, D. S. and Foote, R. M. "Basic Theory of Field Extensions." §13.1 in Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, pp. 510-519, 2004.Cite this as:
Weisstein, Eric W. "Inseparable Extension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/InseparableExtension.html