Meet-irreducible elements in implicative lattices
Author:
Dorothy P. Smith
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
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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.
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Additional Information
Keywords:
Brouwerian lattice,
Heyting algebra,
implicative lattice,
lattice,
meet-irreducible,
relative annihilator,
relative pseudocomplement
Article copyright:
© Copyright 1972
American Mathematical Society