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On subalgebras of Boolean interval algebras

Authors:	Lutz Heindorf

Institution:	Freie Universität Berlin, 2. Mathematisches Institut, Arnimallee 3, D - 141915 Berlin, Germany

Abstract:	We prove that the following three conditions are necessary and sufficient for a Boolean algebra to be embeddable into an interval algebra. (i) is generated by a subset such that $r\cdot s \in \{0,r,s\}$ for all $r,s\in R$ . (ii) has a complemented subalgebra lattice, where complements can be chosen in a monotone way. (iii) is isomorphic to ClopX 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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