power basis over
Let be a number field with and denote the ring of integers of . Then has a power basis over (sometimes shortened simply to power basis) if there exists such that the set is an integral basis for . An equivalent (http://planetmath.org/Equivalent3) condition is that . Note that if such an exists, then and .
Not all rings of integers have power bases. (See the entry biquadratic field for more details.) On the other hand, any ring of integers of a quadratic field has a power basis over , as does any ring of integers of a cyclotomic field. (See the entry examples of ring of integers of a number field for more details.)
|Title||power basis over|
|Date of creation||2013-03-22 15:56:55|
|Last modified on||2013-03-22 15:56:55|
|Last modified by||Wkbj79 (1863)|