A representation theorem for measurable relation algebras with cyclic groups

TL;DR

This paper proves that measurable relation algebras with finite cyclic groups are fully representable and provides a structural description of these algebras.

Contribution

It establishes a representation theorem for a class of measurable relation algebras with finite cyclic groups and offers a structural characterization.

Findings

Measurable relation algebras with finite cyclic groups are completely representable.

Provides a structural description of these algebras.

Extends understanding of the structure of measurable relation algebras.

Abstract

A relation algebra is measurable if the identity element is a sum of atoms, and the square x;1;x of each subidentity atom x is a sum of non-zero functional elements. These functional elements form a group Gx. We prove that a measurable relation algebra in which the groups Gx are all finite and cyclic is completely representable. A structural description of these algebras is also given.