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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Meet-irreducible elements in implicative lattices
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by Dorothy P. Smith
Proc. Amer. Math. Soc. 34 (1972), 57-62
DOI: https://doi.org/10.1090/S0002-9939-1972-0291035-3

Abstract:

A characterization of meet-irreducible elements and atoms in an implicative lattice is obtained and used to derive the following theorems. A complete lattice is implicative and every element has a meet-irreducible decomposition if and only if there are enough principal prime relative annihilator ideals to separate distinct elements. The MacNeille completion of an implicative lattice is an implicative lattice; furthermore the embedding preserves relative pseudocomplements, meet-irreducible elements and atoms.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 57-62
  • MSC: Primary 06A35
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0291035-3
  • MathSciNet review: 0291035