example of an extension that is not normal
In this entry, indicates the real cube root of .
Consider the extension . The minimal polynomial for over is . This polynomial factors in as . Let . Note that . Thus, has no real roots. Therefore, has no roots in since . Hence, has a root in but does not split in . It follows that the extension is not normal.
|Title||example of an extension that is not normal|
|Date of creation||2013-03-22 16:00:28|
|Last modified on||2013-03-22 16:00:28|
|Last modified by||Wkbj79 (1863)|