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.
Fontana, M., HOUSTON E., G., Lucas, T. (2010). Toward a classification of prime ideals in Prüfer domains. FORUM MATHEMATICUM, 22, 741-766 [10.1515/FORUM.2010.041].
Toward a classification of prime ideals in Prüfer domains
FONTANA, Marco;
2010-01-01
Abstract
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.File in questo prodotto:
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