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 =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: / billkinneymath 🔴 Follow me on Instagram: / billkinneymath 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.
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