Power Integral Bases in the Family of Simplest Quartic Fields

DOI10.1080/10586458.2005.10128916zbMath1092.11042OpenAlexW2064616218MaRDI QIDQ5709298

Péter Olajos

Publication date: 29 November 2005

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1128100125

zbMATH Keywords

power integral basisquartic fields

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Cubic and quartic extensions (11R16) Algebraic numbers; rings of algebraic integers (11R04) Multiplicative and norm form equations (11D57)

Related Items (7)

A family of monogenic \(S_4\) quartic fields arising from elliptic curves ⋮ Elliptic curves associated with simplest quartic fields ⋮ Bases of canonical number systems in quartic algebraic number fields ⋮ Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields ⋮ Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields ⋮ Two families of monogenic $S_4$ quartic number fields ⋮ Index, the prime ideal factorization in simplest quartic fields and counting their discriminants

Uses Software

• KANT/KASH

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