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## Main Question or Discussion Point

Could anyone give me some help for showing if K1/F and K2/F are purely inseparable extensions, then K1K2/F is purely inseparable. Thanks!

- Thread starter kavoukoff1
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Could anyone give me some help for showing if K1/F and K2/F are purely inseparable extensions, then K1K2/F is purely inseparable. Thanks!

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Landau

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If E/K is an algebraic extension, then it is purely inseparable iff it is generated by purely inseparable elements.

K1K2/F is generated by the union of the elements by which K1 and K2 are generated.

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