Non cyclic division algebras of prime degree

TL;DR

This paper demonstrates that certain prime degree division algebras are not cyclic by showing their primary components of generic crossed products are not crossed products, providing new examples of non-cyclic division algebras of prime degree.

Contribution

It introduces examples of division algebras of prime degree that are not cyclic, expanding understanding of their structure and properties.

Findings

Primary components of certain generic crossed products are not crossed products.

Examples of division algebras of prime degree that are not cyclic are constructed.

The results apply specifically to prime degree division algebras.

Abstract

This paper shows that $p$ primary components of certain generic crossed products are not crossed products. This applies in particular to primary components of prime degree, thus producing examples of division algebras of prime degree that are not cyclic.