On subalgebras of Boolean interval algebras

Heindorf, Lutz

doi:10.1090/S0002-9939-97-03851-3

On subalgebras of Boolean interval algebras
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Proc. Amer. Math. Soc. 125 (1997), 2265-2274 Request permission

Abstract:

We prove that the following three conditions are necessary and sufficient for a Boolean algebra $A$ to be embeddable into an interval algebra.

$A$ is generated by a subset $R$ such that $r\cdot s \in \{0,r,s\}$ for all $r,s\in R$.
$A$ has a complemented subalgebra lattice, where complements can be chosen in a monotone way.
$A$ is isomorphic to Clop X for a compact zero-dimensional topological semilattice $(X; \cdot )$ such that $x\cdot y\cdot z \in \{x\cdot y, x\cdot z\}$ for all $x,y,z \in X$.

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