Distinguishing division algebras by finite splitting fields

TL;DR

This paper investigates how to distinguish division algebras based on their finite splitting fields, providing criteria to identify when two such algebras are different over specific fields.

Contribution

It introduces methods to determine the uniqueness of division algebras through their finite splitting fields, advancing understanding in algebraic structures.

Findings

Criteria for distinguishing division algebras by finite splitting fields

Conditions under which two central division algebras are distinguishable

Applications to specific field cases

Abstract

This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be distinguished by their finite splitting fields over certain fields.