Geodesic
Atoms, Primes and Implicative Lattices
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 279-285

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DOI

Let L be an a-implicative semilattice. We obtain a characterization of those elements which cover a. This gives a characterization of atoms in pseudocomplemented semilattices, and leads to various results on primes and irreducibles in semilattices. As an application, we prove that in a complete, atomistic lattice L, the following are equivalent (i) L is implicative (ii) L is (2, ∞) meet distributive (iii) each element of L is a meet of primes.
DOI : 10.4153/CMB-1984-042-8
Mots-clés : 06D20, 03G05, 06D15, 03G10 
Hoo, C. S. Atoms, Primes and Implicative Lattices. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 279-285. doi: 10.4153/CMB-1984-042-8
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     title = {Atoms, {Primes} and {Implicative} {Lattices}},
     journal = {Canadian mathematical bulletin},
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     year = {1984},
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     number = {3},
     doi = {10.4153/CMB-1984-042-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-042-8/}
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