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Semisimple completely distributive lattices are Boolean algebras


Author: M. S. Lambrou
Journal: Proc. Amer. Math. Soc. 68 (1978), 217-219
MSC: Primary 06A35; Secondary 06A23
DOI: https://doi.org/10.1090/S0002-9939-1978-0463067-9
Erratum: Proc. Amer. Math. Soc. 73 (1979), 405.
MathSciNet review: 0463067
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Abstract: Semisimple completely distributive lattices are Boolean algebras.


References [Enhancements On Off] (What's this?)

  • [1] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1940. MR 0001959 (1:325f)
  • [2] P. R. Halmos, Lectures on Boolean algebras, Van Nostrand Math. Studies, 1963. MR 0167440 (29:4713)
  • [3] M. S. Lambrou, Complete atomic Boolean lattices, J. London Math. Soc. (2) 15 (1977), 387-390. MR 0444541 (56:2891)
  • [4] W. E. Longstaff, Strongly reflexive lattices, J. London Math. Soc. (2) 11 (1975), 491-498. MR 0394233 (52:15036)
  • [5] G. N. Raney, A sub-direct union representation for completely distributive lattices, Proc. Amer. Math. Soc. 4 (1953), 518-522. MR 0058568 (15:389e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0463067-9
Keywords: Maximal ideals, semisimple, completely distributive, Boolean algebras, atomic
Article copyright: © Copyright 1978 American Mathematical Society

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