purely inseparable extension

purely inseparable extension

[¦pyu̇r·lē in¦sep·rə·bəl ik′sten·chən]
(mathematics)
A purely inseparable extension E of a field F is an algebraic extension of F whose separable degree over F equals 1 or, equivalently, an algebraic extension of F in which every element is purely inseparable over F.