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

Links and resources
===============================

AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.