Krull–Akizuki theorem
= Krull–Akizuki theorem
{wiki=Krull–Akizuki_theorem}
The Krull–Akizuki theorem is a result in the field of commutative algebra, specifically concerning the factorization properties of elements in Noetherian rings. It provides a foundation for understanding how the integral closure of an ideal behaves under certain conditions. More specifically, the theorem considers Noetherian rings and the behavior of ideals in them.