Krull’s principal ideal theorem (Hauptidealsatz)
Let \(R\) be a Noetherian ring and \(a\) an element of \(R\) which is neither a zero divisor nor a unit. Then every minimal prime ideal \(P\) containing \(a\) has height 1 .
Let \(R\) be a Noetherian ring and \(a\) an element of \(R\) which is neither a zero divisor nor a unit. Then every minimal prime ideal \(P\) containing \(a\) has height 1 .