Assume that the number field K contains a primitive n'th root of unity .

Let in the integral ring of K and let I be an prime ideal of the integral ring of K such that is not in I.

Let L=K( ).

Show that is separable modulo I.

Thank you!!!

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- March 11th 2010, 05:02 AMchipaiPrime decomposition in number rings
Assume that the number field K contains a primitive n'th root of unity .

Let in the integral ring of K and let I be an prime ideal of the integral ring of K such that is not in I.

Let L=K( ).

Show that is separable modulo I.

Thank you!!!