Principal ideal rings and a condition of Kummer

DOI10.1016/0021-8693(83)90149-7zbMath0515.13015OpenAlexW1987730342MaRDI QIDQ1051697

Robert Gilmer, William J. Heinzer

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90149-7

zbMATH Keywords

irreducible elementsascending chain conditionBezout ringsK-ringprincipal ideal ringPIR

Mathematics Subject Classification ID

Principal ideal rings (13F10) Commutative Noetherian rings and modules (13E05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items

On a general theory of factorization in integral domains

Cites Work

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• The background of Kummer's proof of Fermat's last theorem for regular primes
• Postscript to The background of Kummer's proof
• Semigroup rings as Prüfer rings
• Unique Factorization of Ideals into Nonfactorable Ideals
• Elementary Divisors and Modules