algebraic integer

Let K be an extensionPlanetmathPlanetmathPlanetmath ( of contained in . A number αK is called an algebraic integerMathworldPlanetmath of K if it is the root of a monic polynomial with coefficients in , i.e., an element of K that is integral over . Every algebraic integer is an algebraic numberMathworldPlanetmath (with K=), but the converseMathworldPlanetmath is false.

Title algebraic integer
Canonical name AlgebraicInteger
Date of creation 2013-03-22 11:45:41
Last modified on 2013-03-22 11:45:41
Owner KimJ (5)
Last modified by KimJ (5)
Numerical id 13
Author KimJ (5)
Entry type Definition
Classification msc 11R04
Classification msc 62-01
Classification msc 03-01
Related topic IntegralBasis
Related topic CyclotomicUnitsAreAlgebraicUnits
Related topic FundamentalUnits
Related topic Monic2
Related topic RingWithoutIrreducibles