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Factoring Ideals in Pr\"ufer Domains

By Marco Fontana, Evan Houston and Tom Lucas

Abstract

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

Topics: Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry
Year: 2006
OAI identifier: oai:arXiv.org:math/0611661

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