Meet-irreducible elements in implicative lattices
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- by Dorothy P. Smith PDF
- Proc. Amer. Math. Soc. 34 (1972), 57-62 Request permission
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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Additional 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