The Boolean ring generated by a distributive lattice
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- by S. J. Bernau PDF
- Proc. Amer. Math. Soc. 32 (1972), 423-424 Request permission
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.References
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- H. M. MacNeille, Extension of a distributive lattice to a Boolean ring, Bull. Amer. Math. Soc. 45 (1939), no. 6, 452–455. MR 1564003, DOI 10.1090/S0002-9904-1939-07007-9 M. H. Stone, Topological representations of distributive lattices and Brouwerian logics, Časopis Pěst. Mat. Fys. 67 (1937), 1-25.
Additional Information
- © Copyright 1972 American Mathematical Society
- 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