minimality of integral basis

The discriminantPlanetmathPlanetmathPlanetmathPlanetmathΔ:=Δ(α1,α2,,αs)  of the set  {α1,α2,,αs}  of integers of an algebraic number fieldMathworldPlanetmath K is a rational integer.  If this set is an integral basis of K, then |Δ| has the least possible (positive integer) value in the field K, and conversely.  The value  d=Δ  is equal for all integral bases of K, and it is called the discriminant or fundamental number of the field.

Title minimality of integral basis
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