Completely split prime
= Completely split prime
A <prime ideal> of a <number field> splits completely in a finite extension of degree $n$ when it factors into $n$ distinct <prime ideals>, each of <residue-field degree> one. In a <Galois extension>, an unramified <prime ideal> splits completely exactly when its <Frobenius conjugacy class> is the identity class. The <Chebotarev density theorem> then gives these primes <Dirichlet density> $1/n$.