Cubic algebras and Implication Algebras

TL;DR

This paper explores the relationship between cubic algebras and implication algebras, introducing functorial constructions, collapses, and a Stone-type representation theorem to deepen understanding of their structure.

Contribution

It provides a functorial method to construct cubic algebras from implication algebras and establishes a collapse process linking the two, culminating in a representation theorem.

Findings

Established a functorial construction from implication to cubic algebras

Defined a collapse process connecting cubic and implication algebras

Proved a Stone-type representation theorem for a class of cubic algebras

Abstract

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra and the connection between these two operations. Finally we use the ideas of the collapse to obtain a Stone-type representation theorem for a large class of cubic algebras.