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Keywords:
Boolean algebra; generalized Boolean algebra; $\frak m$-representability; lattice ordered group; generalized $MV$-algebra; radical class
Boolean algebra; generalized Boolean algebra; $\frak m$-representability; lattice ordered group; generalized $MV$-algebra; radical class
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 $b\in B$, 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.
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