An arithmetic characterization of algebraic number fields with a given class group

DOI10.1017/S0305004100060886zbMath0522.12005MaRDI QIDQ3672085

David E. Rush

Publication date: 1983

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

class numberfactorization of algebraic integersarithmetic characterization of algebraic number fieldscompletely irreducible number

Mathematics Subject Classification ID

Units and factorization (11R27) Iwasawa theory (11R23) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (12)

Systems of sets of lengths. ⋮ On a characterization of algebraic number fields with class number less than three ⋮ On the hfd, chfd, and k-hfd properties in dedekind domains ⋮ A characterization of class groups via sets of lengths ⋮ Half-factorial subrings of factorial domains ⋮ Arithmetical characterizations of divisor class groups ⋮ A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator ⋮ On the local k-elasticities of Puiseux monoids ⋮ AN ARITHMETICAL CHARACTERIZATION OF FINITE ELEMENTARY 2-GROUPS ⋮ Factorization problems in semigroups ⋮ Factorization in Dedekind domains with finite class group ⋮ Arithmetical characterization of class groups of the form \(\mathbb Z/n\mathbb Z\oplus\mathbb Z/n\mathbb Z\) via the system of sets of lengths.

Cites Work

• Arithmetic characterization of algebraic number fields with small class numbers
• A Characterization of Algebraic Number Fields with Class Number Two
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