minimality of integral basis
The discriminant of the set of integers of an algebraic number field is a rational integer. If this set is an integral basis of , then has the least possible (positive integer) value in the field , and conversely. The value is equal for all integral bases of , and it is called the discriminant or fundamental number of the field.
Title | minimality of integral basis |
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Canonical name | MinimalityOfIntegralBasis |
Date of creation | 2013-03-22 15:20:38 |
Last modified on | 2013-03-22 15:20:38 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 9 |
Author | Mathprof (13753) |
Entry type | Theorem |
Classification | msc 11R04 |
Related topic | CanonicalBasis |
Related topic | PropertiesOfDiscriminantInAlgebraicNumberField |
Defines | fundamental number |
Defines | discriminant of field |