On division algebras having the same maximal subfields

TL;DR

This paper investigates conditions under which two finite-dimensional central division algebras over the same field are isomorphic if they share identical maximal subfields.

Contribution

It provides new criteria and insights into when division algebras with the same maximal subfields are necessarily isomorphic.

Findings

Established conditions for isomorphism based on shared maximal subfields

Identified classes of division algebras where sharing maximal subfields implies isomorphism

Extended understanding of the structure of division algebras over various fields

Abstract

We address the problem of when two finite dimensional central division algebras over the same field are necessarily isomorphic given that they have the same maximal subfields.