Galois theory (beginner question about normal algebraic extension: Supposedly Z2(X3)⊂Z2(X)Z2(X3)⊂Z2(X) is not a normal alg extension.)

[Steven G]

Would $x^3-1 = x^3+1=(x-1)(x^2+x+1)= (x+1)(x^2+x+1)$ solve this?

How can you add 1 to x³ and subtract 1 from x³ and expect the results will be equal. After all, x³+1 and x³-1 differ by 2!!!

 

[blamocur]

How can you add 1 to x³ and subtract 1 from x³ and expect the results will be equal. After all, x³+1 and x³-1 differ by 2!!!

They are equal in Z2.