examples of trace and norm

Let ω be a complex root of unity different than 1. Then ω and ω2 are the conjugatePlanetmathPlanetmathPlanetmath roots of the minimal polynomialPlanetmathPlanetmath x2+x+1. Since (ω) is the splitting fieldMathworldPlanetmath of x2+x+1, it is Galois over . Moreover the Galois groupMathworldPlanetmath Gal((ω)/)) is formed by the identityPlanetmathPlanetmath and the automorphismPlanetmathPlanetmathPlanetmath g(ω)=ω2 The elements of (ω) have the form a+bω, a,b. Then we obtain

Title examples of trace and norm
Canonical name ExamplesOfTraceAndNorm
Date of creation 2013-03-22 15:55:45
Last modified on 2013-03-22 15:55:45
Owner polarbear (3475)
Last modified by polarbear (3475)
Numerical id 16
Author polarbear (3475)
Entry type Example
Classification msc 12F05