Reduced Ideals in Pure Cubic Fields

2019/05/01 by G. Tony Jacobs, Jacobs, George · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1905.00242

openalex publication_date 2019/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Reduced ideals have been defined in the context of integer rings in quadratic number fields, and they are closely tied to the continued fraction algorithm. The notion of this type of ideal extends naturally to number fields of higher degree. In the case of pure cubic fields, generated by cube roots of integers, a convenient integral basis provides a means for identifying reduced ideals in these fields. We define integer sequences whose terms are in correspondence with some of these ideals, suggesting a generalization of continued fractions.

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