Toward a classification of prime ideals in Pr\"ufer domains

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Fontana, Marco
Houston, Evan
Lucas, Thomas G.
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Abstract
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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.
Keywords
Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, 13F05, 13A15
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