Dedekind–Kummer theorem
In algebraic number theory, the Dedekind–Kummer theorem describes how a prime ideal in a Dedekind domain factors over the domain's integral closure. Statement for number fields. Let formula_1 be a number field such that formula_2 for formula_3 and let formula_4 be the minimal polynomial for formula_5 over formula_6. For any prime formula_7 not dividing formula_8, writeformula_9where formula_10 are monic irreducible polynomials in formula_11. Then formula_12 factors into prime ideals asformula_13such that formula_14. Statement for Dedekind Domains. See Neukirch.