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
kavoukoff1
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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 x^{pn} and y^{pm} are in F for some m and n. But, how do you use this to show that K1K2/F is a purely inseparable extension?