Toward a classification of prime ideals in Prüfer domains
Authors:
- Marco FontanaMFMarco Fontana
- Evan HoustonEHEvan Houston
- Thomas G. LucasTLThomas G. Lucas
- 1 January 2010
- journal article
- Published by Walter de Gruyter GmbH in Forum Mathematicum
- Vol. 22 (4)
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 theseud five basic properties, there are six types of maximal ideals and twelve types of nonmaximal (nonzero)ud primes. Both characterizations and examples are given for each type that existsKeywords
All Related Versions
This publication has 18 references indexed in Scilit:
- Some properties of divisorial prime ideals in Prüfer domainsJournal of Pure and Applied Algebra, 1986
- Divisorial Prime Ideals in Prüfer DomainsCanadian Mathematical Bulletin, 1984
- Topologically defined classes of commutative ringsAnnali di Matematica Pura ed Applicata (1923 -), 1980
- The S-transform and the ideal transformJournal of Algebra, 1979
- Overrings and divisorial ideals of rings of the form $D+M$.The Michigan Mathematical Journal, 1973
- Integral domains in which each non‐zero ideal is divisorialMathematika, 1968
- Overrings of Prüfer domains. IIJournal of Algebra, 1967
- Overrings of prüfer domainsJournal of Algebra, 1966
- A class of domains in which primary ideals are valuation idealsMathematische Annalen, 1965
- On the ubiquity of Gorenstein ringsMathematische Zeitschrift, 1963