Find a Splitting Field of x^3-1 over ℚ
We find a splitting field for the polynomial f(x)=x^3-1 over the rationals ℚ. It is ℚ(ω), where ω = -1/2 + i*√3/2 = e^(i*2π/3) (and ω^2 = -1/2 - i*√3/2 = e^(i*4π/3)). This splitting field is a degree 2 extension of ℚ because the minimal polynomial of ω over ℚ is x^2 + x + 1, which has degree 2.
#AbstractAlgebra #FieldTheory #SplittingField
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