A Distributivity Condition for Boolean Algebras

Summary:Let $frak m$ be an infinite cardinal. We denote by $C_frak m$ the collection of all $frak m$-representable Boolean algebras. Further, let $C_frak m^0$ be the collection of all generalized Boolean algebras $B$ such that for each $bin B$, the interval $[0,b]$ of $B$ belongs to $C_frak m$. In this paper we prove that $C_frak m^0$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized $MV$-algebras