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arXiv · 1806.10035

Krull's Principal Ideal Theorem in non-Noetherian settings

Bruce Olberding
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Abstract

Let $P$ be a finitely generated ideal of a commutative ring $R$. Krull's Principal Ideal Theorem states that if $R$ is Noetherian and $P$ is minimal over a principal ideal of $R$, then $P$ has height at most one. Straightforward examples show that this assertion fails if $R$ is not Noetherian. We consider what can be asserted in the non-Noetherian case in place of Krull's theorem.

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Bruce Olberding. 2018-06-26. Krull's Principal Ideal Theorem in non-Noetherian settings. https://doi.org/10.1017/s0305004118000531

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