Norms and Cayley Hamilton algebras

TL;DR

This paper develops a comprehensive theory of Cayley Hamilton algebras based on norms, extending previous trace-based approaches limited to characteristic zero, and compares these methods.

Contribution

It introduces a general framework for Cayley Hamilton algebras using norms, broadening the scope beyond characteristic zero trace methods.

Findings

Established a norm-based theory for Cayley Hamilton algebras.

Compared norm-based approach with trace-based methods in characteristic zero.

Extended the understanding of Cayley Hamilton algebras to more general settings.

Abstract

We develop the general Theory of Cayley Hamilton algebras using norms and compare with the approach, valid only in characteristic 0, using traces and presented in a previous paper $T$-ideals of Cayley Hamilton algebras, 2020, arXiv:2008.02222