Marco Fontana, Evan Houston, Thomas G. Lucas
Published 2008-10-14Version 1
The primary purpose of this paper is give a classification scheme for the nonzero primes of a Pr\"ufer domain based on five properties. A prime $P$ of a Pr\"ufer domain $R$ could be sharp or not sharp, antesharp or not, divisorial or not, branched or unbranched, idempotent or not. Based on these five basic properties, there are six types of maximal ideals and twelve types of nonmaximal (nonzero) primes. Both characterizations and examples are given for each type that exists.
Properties of chains of prime ideals in an amalgamated algebra along an ideal
On completely decomposable and separable modules over Prüfer domains
Multidegrees, prime ideals, and non-standard gradings
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