MathNugget
Junior Member
- Joined
- Feb 1, 2024
- Messages
- 195
Supposedly Z2(X3)⊂Z2(X) is not a normal alg extension. I know by 1 definition that means if an irreducible polynomial from first field has a root in the 2nd, then it has all the roots in the 2nd.
Would x3−1=x3+1=(x−1)(x2+x+1)=(x+1)(x2+x+1) solve this? the last polynomial doesn't have any root in Z2(X), so it would be an example to prove that is not a normal extension...
Would x3−1=x3+1=(x−1)(x2+x+1)=(x+1)(x2+x+1) solve this? the last polynomial doesn't have any root in Z2(X), so it would be an example to prove that is not a normal extension...