There was an answered question in the morning but it is erased. Could you help me on that question.

"Let be a primitive n-th root of unity over , where n>2 and let . Prove that is algebraic over of degree "

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- Apr 25th 2010, 08:23 PMsuperman123primitive n-th root
There was an answered question in the morning but it is erased. Could you help me on that question.

"Let be a primitive n-th root of unity over , where n>2 and let . Prove that is algebraic over of degree " - Apr 25th 2010, 09:48 PMBruno J.
Consider the polynomial . Its roots are and therefore is of degree over . What do you conclude?

- Apr 25th 2010, 10:10 PMBruno J.
Here's another proof. Let . Let . It's easy to see that is the fixed field of the subgroup where (prove this!). Therefore .

- Apr 25th 2010, 10:38 PMsuperman123
- Apr 25th 2010, 10:54 PMsuperman123
I am trying to understand splitting fields. Are these fields same?

- Apr 25th 2010, 11:24 PMBruno J.
- Apr 25th 2010, 11:40 PMsuperman123