A representation theorem for measurable relation algebras with cyclic groups
Hajnal Andréka, Steven R. Givant · Transactions of the American Mathematical Society · 2019
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 $G_x$. We prove that a measurable relation algebra in which the groups $G_x$ are all finite and cyclic is completely representable. A structural description of these algebras is also given.