On the arithmetic of certain not integrally closed noetheian integral domains

DOI10.1080/00927879108824164zbMath0723.20038OpenAlexW1974879893MaRDI QIDQ3211534

Alfred Geroldinger

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1080/00927879108824164

zbMATH Keywords

irreducible elementsKrull domainsmultiplicative semigroupsets of lengthslengths of factorizationsfinite Picard groupfinitely related semigroupnoetherian integral domainsnonintegrally closed noetherian domainssemigroup with divisor homomorphism

Mathematics Subject Classification ID

Commutative semigroups (20M14) Integral domains (13G05) Semigroup rings, multiplicative semigroups of rings (20M25) Divisibility and factorizations in commutative rings (13A05)

Related Items (17)

Delta sets for symmetric numerical semigroups with embedding dimension three ⋮ General w-ZPI-Rings and a Tool for Characterizing Certain Classes of Monoid Rings ⋮ Properties of factorizations with successive lengths in one-dimensional local domains ⋮ Chains of factorizations and sets of lengths ⋮ Factorization of powers in \(C\)-monoids. ⋮ T-block monoids and their arithmetical applications to certain integral domains ⋮ Shifts of generators and delta sets of numerical monoids ⋮ Elasticity of factorizations in atomic monoids and integral domains ⋮ Length-factoriality in commutative monoids and integral domains ⋮ Computation of delta sets of numerical monoids. ⋮ Delta sets for nonsymmetric numerical semigroups with embedding dimension three ⋮ Beyond Coins, Stamps, and Chicken McNuggets: An Invitation to Numerical Semigroups ⋮ On parametrized families of numerical semigroups ⋮ Factorization in finitely generated domains. ⋮ Delta Sets of Numerical Monoids Using Nonminimal Sets of Generators ⋮ Numerical Semigroups on Compound Sequences ⋮ On lengths of non-unique factorizations and systems of linear diophantine inequalities

Cites Work

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• Factorization problems in semigroups
• Commutative rings in which every ideal is a product of primary ideals
• On non-unique factorizations into irreducible elements
• On primary factorizations
• Subsemigroups of finitely generated groups with divisor-theory
• Noetherian Rings in Which Every Ideal is a Product of Primary Ideals
• Krull Semigroups and Divisor Class Groups

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