The Cyclicity of Tensor Products of Cyclic $p$-Algebras

TL;DR

This paper revisits Albert's theorem on cyclicity of tensor products of cyclic p-algebras, providing explicit computations for prime degree cases in symbol algebra terms.

Contribution

It offers an explicit computation method for tensor products of cyclic p-algebras of prime degree, enhancing understanding of their structure.

Findings

Explicit computation of tensor products as cyclic algebras

Representation of resulting algebras in symbol algebra form

Clarification of cyclicity conditions for prime degree cases

Abstract

We revisit the famous theorem of Albert's on the cyclicity of tensor products of cyclic $p$-algebras. In the case of tensor products of cyclic $p$-algebras of prime degree, we provide an explicit computation of the resulting cyclic algebra in symbol algebra terms.