On Dedekind domains whose class groups are direct sums of cyclic groups

DOI10.1016/j.jpaa.2023.107470zbMath1520.13026arXiv2305.18796OpenAlexW4380202458MaRDI QIDQ6132837

Gyu Whan Chang, Alfred Geroldinger

Publication date: 17 August 2023

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.18796

zbMATH Keywords

ordersclass groupDedekind domains

Mathematics Subject Classification ID

Ideal theory for semigroups (20M12) Semigroup rings, multiplicative semigroups of rings (20M25) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Class groups (13C20) Divisibility and factorizations in commutative rings (13A05)

Related Items (1)

Polynomial Dedekind domains with finite residue fields of prime characteristic

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic Dedekind domains revisited
• Combinatorial number theory and additive group theory. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse)
• Direct summands of class groups
• Répartition des idéaux premiers parmi les classes d'idéaux dans un anneau de Dedekind et équidécomposition. (Distribution of prime ideals within the ideal classes in a Dedekind ring and equidecomposition.)
• Realization theorems for semigroups with divisor theory
• On the ideal class group problem for global fields
• On the class group of a graded domain
• The characterization of finite elasticities. Factorization theory in Krull monoids via convex geometry
• On congruence half-factorial Krull monoids with cyclic class group
• Every Abelian group is a class group
• On the distribution of prime divisors in Krull monoid algebras
• The set of minimal distances in Krull monoids
• A Note on Conductor Ideals
• Some Recent Results and Open Problems on Sets of Lengths of Krull Monoids with Finite Class Group
• Every abelian group is the class group of a simple Dedekind domain
• Multiplicative ideal theory in the context of commutative monoids
• More Noneuclidian PID's and Dedekind Domains with Prescribed Class Group
• On c-semigroups
• The monoid of regular elements in commutative rings with zero divisors
• On the distribution of prime divisors in class groups of affine monoid algebras
• The Class Group of Dedekind Domains
• Polynomial Dedekind domains with finite residue fields of prime characteristic

This page was built for publication: On Dedekind domains whose class groups are direct sums of cyclic groups