Important Consequences
The Chebotarev density theorem reduces the problem of classifying Galois extensions of a number field to that of describing the splitting of primes in extensions. Specifically, it implies that as a Galois extension of K, L is uniquely determined by the set of primes of K that split completely in it. A related corollary is that if almost all prime ideals of K split completely in L, then in fact L = K.
Read more about this topic: Chebotarev's Density Theorem
Famous quotes containing the words important and/or consequences:
“What’s important is promising something to the people, not actually keeping those promises.... The people have always lived on hope alone.”
—Hermann Broch (1886–1951)
“There are more consequences to a shipwreck than the underwriters notice.”
—Henry David Thoreau (1817–1862)