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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Boolean ring generated by a distributive lattice


Author: S. J. Bernau
Journal: Proc. Amer. Math. Soc. 32 (1972), 423-424
MSC: Primary 06A40
DOI: https://doi.org/10.1090/S0002-9939-1972-0292728-4
MathSciNet review: 0292728
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Abstract: This note gives a simple characterization of the Boolean ring R generated by a distributive lattice L. The method is to introduce a Hausdorff topology on the Stone representation space E of L and note that R is the set of subsets of E which are compact and open with respect to this topology.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292728-4
Keywords: Distributive lattice, Stone representation space, dual hull-kernel topology, embedding in a Boolean ring
Article copyright: © Copyright 1972 American Mathematical Society