Kummer-Dedekind's factorisation theorem

Question

For a number field extension $K$ of $\mathbb{Q}$ one can factorise almost all prime ideals $(p)$ in the extension $K$, except finitely many, easily by factorising minimal polynomials in finite fields.

Is there a simply written reference for the precise statement of this result stated for extensions $K/L$ where $L$ is a general number field rather than $\mathbb{Q}$?

I know that the interesting problem is that of factorising every prime ideal in the extension but here I am only interested in having a simple and nice statement that works for not necessarily all primes.

Answer 1

Here is the general statement as presented in Neukirch's Algebraic Number Theory, p.47-48: