quasi
Posts:
11,714
Registered:
7/15/05


Re: about the KroneckerWeber theorem
Posted:
Feb 4, 2013 4:04 AM


David Bernier wrote: > >I have a further question about conjugate roots ... > >The nontrivial third roots of unity >1/2 +i*srqrt(3)/2 and 1/2 i*srqrt(3)/2 >are complex conjugates. > >I don't know of a definition where, for example, in the >setting above, >2^(1/3) is said to be conjugate to >2^(1/3) * (1/2 +i*srqrt(3)/2).
Let H be an algebraically closed field, and let K be a subfield of H. Let K[x] denote the ring of all polynomials in the indeterminate x with coefficients in K. If f in K[x] is irreducible in K[x], the roots of f in H are said to be conjugates of each other over K.
Thus, the 3 cube roots of 2 are conjugate over Q since they are roots of the polynomial x^3  2 which is irreducible over Q.
quasi

