On relative pure cyclic fields with power integral bases

DOI10.21136/MB.2022.0142-21OpenAlexW4224983150MaRDI QIDQ5878485

Mohammed Sahmoudi, Mohamed El Hassani Charkani

Publication date: 21 February 2023

Published in: Mathematica Bohemica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/mb.2022.0142-21

zbMATH Keywords

discrete valuation ringDedekind ringmonogenityrelative integral basisnonic field

Mathematics Subject Classification ID

Other number fields (11R21) Algebraic number theory computations (11Y40) Cubic and quartic extensions (11R16) Algebraic numbers; rings of algebraic integers (11R04) Algebraic number theory: global fields (11Rxx)

Cites Work

• Generating a power basis over a Dedekind ring
• Lifting monogenic cubic fields to monogenic sextic fields
• On Dedekind's criterion and monogenicity over Dedekind rings
• On criteria by Dedekind and Ore for integral ring extensions
• A relative integral basis over \(\mathbb{Q}(\sqrt{-3})\) for the normal closure of a pure cubic field
• On power integral bases of unramified cyclic extensions of prime degree
• Relative integral bases for quartic fields over quadratic subfields
• On relative power integral basis of a family of numbers fields
• On Integral Bases
• A Generalization of Dedekind Criterion
• A Note on Elliptic Curves and the Monogeneity of Rings of Integers
• Relative Integral Bases
• Tower Index formula and monogenecity
• Power integral bases in cubic and quartic extensions of real quadratic fields
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