Integral basis of cubic number fields

DOI10.1515/9783110213188.213zbMATH Open1222.11125arXiv0907.2786OpenAlexW2480414861MaRDI QIDQ3653964

Lhoussain El Fadil

Publication date: 4 January 2010

Published in: Commutative Algebra and its Applications (Search for Journal in Brave)

Abstract: In this paper, based on techniques of Newton polygons, a result which allows the computation of a p integral basis of every quartic number field is given. For each prime integer p, this result allows to compute a p-integral basis of a quartic number field K defined by an irreducible polynomial $P(X)=X4+aX+binz[X]$ in methodical and complete generality.

Full work available at URL: https://arxiv.org/abs/0907.2786

zbMATH Keywords

Newton polygonnumber fields\(p\)-integral bases, index

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16)

Related Items (4)

EFFECTIVE DETERMINATION OF PRIME DECOMPOSITIONS OF CUBIC FUNCTION FIELDS ⋮ An explicit triangular integral basis for any separable cubic extension of a function field ⋮ A relative integral basis over \(\mathbb{Q}(\sqrt{-3})\) for the normal closure of a pure cubic field ⋮ Ideal arithmetic and infrastructure in purely cubic function fields

Recommendations

• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• On bases of purely cubic fields over quadratic fields 👍 👎
• Cubic fields with a power basis 👍 👎
• Cubic Fields and Radical Extensions 👍 👎
• 𝑝-integral bases of a cubic field 👍 👎
• Computation of a power integral basis of a pure cubic number field 👍 👎

This page was built for publication: Integral basis of cubic number fields

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3653964)