Ideal classes of orders in quaternion algebras

Stefano Marseglia; Harry Smit; John Voight

doi:10.1016/j.jpaa.2024.107649

Ideal classes of orders in quaternion algebras

Stefano Marseglia^*, Harry Smit, John Voight

^*Corresponding author for this work

Dartmouth College

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We provide an algorithm that, given any order O in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right O-ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras.

Original language	English
Article number	107649
Journal	Journal of Pure and Applied Algebra
Volume	228
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2024.107649
Publication status	Published - Jul 2024

Keywords

Algorithms
Ideal classes
Orders
Quaternion algebras

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10.1016/j.jpaa.2024.107649Licence: CC BY

1-s2.0-S002240492400046X-mainFinal published version, 519 KBLicence: CC BY

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title = "Ideal classes of orders in quaternion algebras",

abstract = "We provide an algorithm that, given any order O in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right O-ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras.",

keywords = "Algorithms, Ideal classes, Orders, Quaternion algebras",

author = "Stefano Marseglia and Harry Smit and John Voight",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

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AU - Marseglia, Stefano

AU - Smit, Harry

AU - Voight, John

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AB - We provide an algorithm that, given any order O in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right O-ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras.

KW - Algorithms

KW - Ideal classes

KW - Orders

KW - Quaternion algebras

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DO - 10.1016/j.jpaa.2024.107649

M3 - Article

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SN - 0022-4049

VL - 228

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 7

M1 - 107649

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Ideal classes of orders in quaternion algebras

Abstract

Keywords

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