purely inseparable extension

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purely inseparable extension [¦pyu̇r·lē in¦sep·rə·bəl ik′sten·chən]

(mathematics)

A purely inseparable extensionEof a fieldFis an algebraic extension ofFwhose separable degree overFequals 1 or, equivalently, an algebraic extension ofFin which every element is purely inseparable overF.

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