A survey of non-complex analogs of uniform algebras

TL;DR

This paper surveys various analogs of uniform algebras across Archimedean, non-Archimedean, commutative, and non-commutative settings, highlighting constraints and examples in these mathematical frameworks.

Contribution

It provides a comprehensive overview of non-complex uniform algebras, including new examples and discussion of development constraints.

Findings

Includes non-Archimedean examples of uniform algebras

Discusses constraints on non-complex uniform algebra development

Provides a comparative survey across different algebraic settings

Abstract

We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.