Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings

DOI10.1016/0021-8693(87)90226-2zbMath0641.13003OpenAlexW2027745368MaRDI QIDQ1100514

B. George

Publication date: 1987

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90226-2

zbMATH Keywords

idealssublatticesPrüfer ring

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items

Idealization of a module, Valuative rings, Radical factorization in commutative rings, monoids and multiplicative lattices, Invertibility, Semistar Operations, and the Ring of Finite Fractions, Uniserial modules over manis rings, Hochster’ theorem, coherent locales, and lattices of radical ideals, Strong Prüfer rings and the ring of finite fractions, Dilworth's principal elements, Constructions of manis valuation rings

Cites Work

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• The rings R(X) and \(R<X>\)
• Abstract commutative ideal theory
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• Arithmetically embeddable local Noether lattices
• Abstract commutative ideal theory without chain condition
• Structure theorems for regular local Noether lattices
• Krull rings with zero divisors
• Generalizations of Multiplicative Ideal Theory to Commutative Rings with Zerodivisors
• Two annihilator conditions:property(A)and(A.C.)
• Characterizing prüfer rings via their regular ideals
• The generalized Kronecker function ring and the ring R(X).
• Overrings of Commutative Rings. II. Integrally Closed Overrings
• Prüfer rings with zero divisors.
• Principal Elements of Lattices of Ideals
• On Prüfer rings
• Valuations and Prufer Rings