The characterization of cyclic cubic fields with power integral bases

DOI10.2996/kmj44204zbMath1478.11126arXiv1912.03103OpenAlexW3175346606MaRDI QIDQ1984262

Ryutaro Sekigawa, Tomokazu Kashio

Publication date: 13 September 2021

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

Full work available at URL: https://arxiv.org/abs/1912.03103

zbMATH Keywords

power integral basiscyclic cubic fieldssimplest cubic fieldsmonogenic number fieldsShank's polynomials

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Cubic and quartic Diophantine equations (11D25) Algebraic numbers; rings of algebraic integers (11R04) Galois cohomology (11R34)

Related Items (3)

Unit reducible fields and perfect unary forms ⋮ On the monogenicity of power-compositional Shanks polynomials ⋮ Rikuna's generic cyclic polynomial and the monogenity

Cites Work

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• On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields
• Extensions cubiques cycliques de \(\mathbb{Q}\) dont l'anneau des entiers est monogene
• The Simplest Cubic Fields
• On the Class Number of a Relatively Cyclic Number Field

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