Purely Inseparable Extensions

  • Thread starter kavoukoff1
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  • #1

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!
 

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  • #2
Sorry, I forgot to put up my thoughts/attempts at this problem. Do I use the fact that if x is an element of K1 and y is an element of K2, then xpn and ypm are in F for some m and n. But, how do you use this to show that K1K2/F is a purely inseparable extension?
 
  • #3
Landau
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This is not my area of expertise, but here's a thought:

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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