Factoring Ideals in Prüfer Domains

Details Factoring Ideals in Prüfer Domains Factoring Ideals in Prüfer Domains

2006-11-21

arxiv.org/abs/math/0611661v1

Mathematics

Commutative Algebra

Scientific paper

We show that in certain Pr\"ufer domains, each nonzero ideal $I$ can be factored as $I=I^v \Pi$, where $I^v$ is the divisorial closure of $I$ and $\Pi$ is a product of maximal ideals. This is always possible when the Pr\"ufer 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 Pr\"ufer domains. We also explore consequences of these factorizations and give illustrative examples.

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