When the dual of an ideal is a ring

DOI10.1007/BF01239947zbMath0484.13001MaRDI QIDQ1163594

James A. Huckaba, Ira J. Papick

Publication date: 1982

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154830

zbMATH Keywords

integral domaindivisorial idealPruefer domaindual of idealnon-invertible prime ideal

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05)

Related Items (35)

Trace Properties and Integral Domains, II ⋮ Duals and Transforms of Ideals in PVMDs ⋮ Strongly divisorial ideals and complete integral closure of an integral domain ⋮ Revisiting G-Dedekind domains ⋮ On divisorial prime ideals in Prüfer v-multiplication domains ⋮ Domains satisfying the trace property ⋮ Trace Properties and Pullbacks ⋮ The radical trace property ⋮ RATLIFF–RUSH CLOSURE OF IDEALS IN INTEGRAL DOMAINS ⋮ Unnamed Item ⋮ Jónsson extensions of one-dimensional semilocal domains ⋮ Core of ideals in one-dimensional Noetherian domains ⋮ Integral domains with Boolean \(t\)-class semigroup ⋮ Almost principal ideals in \(\mathrm R[x\)] ⋮ Core of ideals in integral domains ⋮ Divisorial Prime Ideals in Prüfer Domains ⋮ Reductions and Core of Ideals in Integral Domains: Some Recent Developments ⋮ Noetherian domains in which every ideal is isomorphic to a trace ideal ⋮ THE v-OPERATION IN EXTENSIONS OF INTEGRAL DOMAINS ⋮ When is the dual of an ideal a ring? ⋮ Trace properties in rings with zero divisors ⋮ Quasi-Baer module hulls and their examples ⋮ Quasi-Baer module hulls and applications ⋮ Toward a classification of prime ideals in Prüfer domains ⋮ Star operations in extensions of integral domains ⋮ On the set of \(t\)-linked overrings of an integral domain ⋮ Divisorial behavior of prime ideals in Prüfer domains ⋮ t-class semigroups of integral domains ⋮ Constituent groups of Clifford semigroups arising from \(t\)-closure ⋮ Globalizing local properties of Prüfer domains ⋮ The \(S\)-transform and its dual with applications to Prüfer extensions ⋮ Invertible and divisorial ideals of generalized Dedekind domains ⋮ Some remarks on divisorial and seminormal overrings ⋮ TW-domains and strong Mori domains ⋮ Some properties of divisorial prime ideals in Prüfer domains

Cites Work

• Overrings of Prüfer domains. II
• On the prime ideals of the ring of entire functions
• Unnamed Item
• Unnamed Item

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