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Factoring ideals in Prüfer domains
Authors:Marco Fontana  Thomas Lucas
Affiliation:a Dipartimento di Matematica, Università degli Studi Roma Tre, Largo San L. Murialdo, 1, 00146 Roma, Italy
b Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Abstract:We show that in certain Prüfer domains, each nonzero ideal I can be factored as View the MathML source, where Iv is the divisorial closure of I and View the MathML source 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.
Keywords:Primary, 13F05   secondary, 13A15
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