Re: Split or Irreducible


Arturo Magidin wrote:
> In article <1114115251.075767.199410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> <jamesdickerson00@xxxxxxxxxxx> wrote:
> >Let E be a subset of the Complex numbers and assume r=e^(2*pi*i)/p
be
> >in E where p is a prime number. Let a be arbitrary in E. Show that
> >the polynomial f(x)=(x^p)-a is irreducible or splits in E[x].
> >
> >I know that r must be the key to the problem but I don't know how to
> >use it.
>
> E is a "subset" of C? Just a subset? We're not assuming closed under
> products, sums, anything?
>
> I assume you mean "subfield"... Assuming that:
>
> If u is a root for f(x), how much is f(ru)?

I mistyped that. I did mean subfield. f(ru)=(ru)^p-a.

Do I need to use the fact that
u=e^(2*pi*i)/p=cos(2*pi/p)+i*sin(2*pi/p)?

James

.