Functional continuity of unital $B_{0}$-algebras with orthogonal bases

TL;DR

This paper proves that in unital $B_{0}$-algebras with orthogonal bases, all multiplicative linear functionals are continuous, resolving a previously posed mathematical problem.

Contribution

It establishes the continuity of multiplicative linear functionals in unital $B_{0}$-algebras with orthogonal bases, answering a question by Sawon and Wronski.

Findings

All multiplicative linear functionals are continuous in the specified algebras.

Provides a positive answer to a problem posed by Sawon and Wronski.

Enhances understanding of the structure of $B_{0}$-algebras with orthogonal bases.

Abstract

Let $A$ be a unital $B_{0}$-algebra with an orthogonal basis, then every multiplicative linear functional on $A$ is continuous. This gives an answer to a problem posed by Z. Sawon and Z. Wronski.