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Factoring Ideals in Prüfer Domains

Marco Fontana·Evan Houston·Tom Lucas
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Abstract

We show that in certain Prüfer domains, each nonzero ideal $I$ can be factored as $I=I^v Π$, where $I^v$ is the divisorial closure of $I$ and $Π$ is a product of maximal ideals. This is always possible when the Prüfer domain is $h$-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the $h$-local property in Prüfer domains. We also explore consequences of these factorizations and give illustrative examples.

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Marco Fontana, Evan Houston, Tom Lucas. 2006-11-21. Factoring Ideals in Prüfer Domains. https://arxiv.org/abs/math/0611661

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