π-domains, overrings, and divisorial ideals

DOI10.1017/S001708950000361XzbMath0379.13011OpenAlexW2113434968MaRDI QIDQ4159465

Daniel D. Anderson

Publication date: 1978

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s001708950000361x

Mathematics Subject Classification ID

Integral domains (13G05) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15)

Related Items

General w-ZPI-Rings and a Tool for Characterizing Certain Classes of Monoid Rings ⋮ \(t\)-linked extensions, the \(t\)-class group, and Nagata's theorem ⋮ FACTORABLE DOMAINS ⋮ Locally almost factorial integral domains ⋮ Module-Theoretic Characterizations of Generalized GCD Domains ⋮ Some characterizations of Krull domains ⋮ A new characterization of GCD domains of formal power series ⋮ On t-invertibility ⋮ Generalized GCD rings. IV ⋮ On S-GCD domains ⋮ Unique factorization and S-Picard groups of domains of power series ⋮ Globalization of Some Local Properties in Krull Domains ⋮ Some Remarks on Generalized GCD Domains ⋮ The local \(S\)-class group of an integral domain ⋮ Divisible Is Injective over Krull Domains ⋮ Riesz and pre-Riesz monoids ⋮ Formal power series rings over a \(\pi \)-domain ⋮ NEW CHARACTERIZATIONS OF GENERALIZED DEDEKIND PRIME RINGS ⋮ Unique factorization of ideals in commutative rings with zero divisors ⋮ Locally factorial integral domains ⋮ Weak π-rings ⋮ Domains whose ideals meet a universal restriction

Cites Work

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• Every Abelian group is a class group
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• On flat overrings, ideal transforms and generalized transforms of a commutative ring
• A Characterization of General Z.P.I.-Rings
• Prime Ideals in GCD-Domains