In a Noetherian ring, a principal nonzerodivisor cuts codimension one.Suggest a slogan
Let \(R\) be a commutative Noetherian ring and let \(a\in R\) be neither a zero divisor nor a unit. Then every prime ideal \(\mfp\) minimal among the prime ideals containing \(a\) has height \(1\).
What is Krull's Hauptidealsatz?