|
|
|
|
|
Hilbert's Theorem 90In number theory, Hilbert's Theorem 90 tells us that if L/K is a cyclic extension of number fields generated by an element s and if α is an element of L of relative norm 1, then then there exists β in L such that - α = β/βs.
The theorem has its most natural statement in terms of group cohomology, where if G is the Galois group - Gal(L/K)
of L over K, and Lx is the multiplicative group of L, then the first cohomology group is trivial: - H1(G, Lx) = {1}.
The theorem takes its name from the fact that it is the 90th theorem in Hilbert's famous Zahlbericht of 1897. Often a more general theorem is given the name, stating that if L/K is a finite Galois extension of fields, then the first cohomology group is trivial; - H1(G, Lx) = {1}
remains true.
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|