example of normal extension
Now, let denote the positive real fourth root of and define . Then the extension is normal because is the splitting field of , and as before is a Galois extension with .
However, the extension is neither normal nor Galois. Indeed, the polynomial has one root in (actually two), namely , and yet does not split in into linear factors.
The Galois closure of over is .
|Title||example of normal extension|
|Date of creation||2013-03-22 14:30:46|
|Last modified on||2013-03-22 14:30:46|
|Last modified by||alozano (2414)|