Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0292728
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] S. J. Bernau, Topologies on structure spaces of lattice groups, Pacific J. Math. (to appear). MR 0316341 (47:4889)
  • [2] G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R.I., 1967. MR 37 #2638. MR 0227053 (37:2638)
  • [3] F. Hausdorff, Mengenlehre, 2nd ed., de Gruyter, Berlin, 1927.
  • [4] J. L.Kelley, General topology, Van Nostrand, Princeton, N.J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [5] H. M. MacNeille, Extension of a distributive lattice to a Boolean ring, Bull. Amer. Math. Soc. 45 (1939), 452-455. MR 1564003
  • [6] M. H. Stone, Topological representations of distributive lattices and Brouwerian logics, Časopis Pěst. Mat. Fys. 67 (1937), 1-25.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A40

Retrieve articles in all journals with MSC: 06A40

Additional Information

Keywords: Distributive lattice, Stone representation space, dual hull-kernel topology, embedding in a Boolean ring
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society