Abst Alg, Lec 33B: Field Extensions, Splitting Fields, Fundamental Theorem of Field Theory, Examples

[@garrettvanbeek9309]

This video is great! I went from being lost in my AA textbook to seeing the beauty of splitting fields. People like Bill Kinney are why I love the internet. Keep up the good work!

[@billkinneymath]

Thanks! So glad it was helpful for you. It was always a hard topic for me when I was first learning it.

[@zacharysmith8156]

That last argument you made about closure under multiplication was awesome.

[@propoop6991]

shouldnt the splitting field in the final minute be Q(sqrt(3) i) ?

[@billkinneymath]

Yes. That's a different way to represent the same answer.

[@bulebegins]

Why is there a light switch on the white board!!?

[@billkinneymath]

Good question. But I'm glad there was. It was very convenient.

[@1tecladocasio]

to turn it black hehehe.

[@obentabiayuk4780]

please how do i prove that Q[sqrt2] is a subfield of R

[@rarjun8793]

Can u please give me the solution on splitting field of f(x)=x^2+x+1€Z(x)

[@billkinneymath]

One way to write the splitting field for this polynomial over the rationals ℚ is as ℚ(-1/2+sqrt(3)*i/2). You could also simplify this to ℚ(sqrt(3)*i).