Abstract
AbstractLetPbe a finitely generated ideal of a commutative ringR. Krull's principal ideal theorem states that ifRis Noetherian andPis minimal over a principal ideal ofR, thenPhas height at most one. Straightforward examples show that this assertion fails ifRis not Noetherian. We consider what can be asserted in the non-Noetherian case in place of Krull's theorem.
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More From: Mathematical Proceedings of the Cambridge Philosophical Society
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