Integral embeddings of central simple algebras over number fields

TL;DR

This paper provides a criterion for embedding orders of maximal subfields into orders of central simple algebras over number fields, generalizing and recovering previous results in the field.

Contribution

It introduces a new criterion that precisely determines when such embeddings are possible, extending prior work and unifying existing results.

Findings

Established a clear criterion for embeddings of maximal subfield orders

Generalized previous embedding results in the context of central simple algebras

Unified various earlier findings through this new criterion

Abstract

A criterion for determining exactly when an order of a maximal subfield of a central simple algebra over a number field can be embedded into an order of this algebra is given. Various previous results have been generalized and recovered by applying this criterion.