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.
Fontana, M., HOUSTON EVAN, G., Lucas, T. (2007). Factoring Ideals in Prüfer Domains. JOURNAL OF PURE AND APPLIED ALGEBRA, 211, 1-13 [10.1016/j.jpaa.2006.12.011].
Factoring Ideals in Prüfer Domains
FONTANA, Marco;
2007-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
