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On subalgebras of Boolean interval algebras


Author: Lutz Heindorf
Journal: Proc. Amer. Math. Soc. 125 (1997), 2265-2274
MSC (1991): Primary 06E05; Secondary 54F05
DOI: https://doi.org/10.1090/S0002-9939-97-03851-3
MathSciNet review: 1389523
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Abstract: We prove that the following three conditions are necessary and sufficient for a Boolean algebra $A$ to be embeddable into an interval algebra.

(i)
$A$ is generated by a subset $R$ such that $r\cdot s \in \{0,r,s\}$ for all $r,s\in R$.
(ii)
$A$ has a complemented subalgebra lattice, where complements can be chosen in a monotone way.
(iii)
$A$ 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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Additional Information

Lutz Heindorf
Affiliation: Freie Universität Berlin, 2. Mathematisches Institut, Arnimallee 3, D - 141915 Berlin, Germany
Email: heindorf@math.fu-berlin.de

DOI: https://doi.org/10.1090/S0002-9939-97-03851-3
Received by editor(s): November 1, 1995
Received by editor(s) in revised form: March 11, 1996
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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