Maximal orders optimal embedding of central simple algebras over number fields

Yuxuan Yang

Maximal orders optimal embedding of central simple algebras over number fields

Number Theory 2026-04-01 v2 Rings and Algebras

Authors: Yuxuan Yang

Abstract

Given a number field $F$ and $R$ be the ring of integers of $F$ , the problem of embedding a field extension $K/F$ into a central simple algebra $B$ is classical. This paper proves that when the central simple algebra has degree $p$ , the $R$ -order $S\subset K$ can be optimal embedded into all maximal $R$ -orders $O\subset B$ , unless satisfies the optimal selectivity condition.

Keywords

metric embeddings fields

Cite

@article{arxiv.2511.21137,
  title  = {Maximal orders optimal embedding of central simple algebras over number fields},
  author = {Yuxuan Yang},
  journal= {arXiv preprint arXiv:2511.21137},
  year   = {2026}
}

Comments

There is a fundamental error in Theorem 3.5 of the paper

Related papers

View all related →