Geodesic
Doubling Constructions in Lattice Theory
Canadian journal of mathematics, Tome 44 (1992) no. 2, pp. 252-269

Voir la notice de l'article provenant de la source Cambridge University Press

This paper examines the simultaneous doubling of multiple intervals of a lattice in great detail. In the case of a finite set of W-failure intervals, it is shown that there in a unique smallest lattice mapping homomorphically onto the original lattice, in which the set of W-failures is removed. A nice description of this new lattice is given. This technique is used to show that every lattice that is a bounded homomorphic image of a free lattice has a projective cover. It is also used to give a sufficient condition for a fintely presented lattice to be weakly atomic and shows that the problem of which finitely presented lattices are finite is closely related to the problem of characterizing those finite lattices with a finite W-cover.
DOI : 10.4153/CJM-1992-017-7
Mots-clés : 06B25, 06B05 
Day, Alan. Doubling Constructions in Lattice Theory. Canadian journal of mathematics, Tome 44 (1992) no. 2, pp. 252-269. doi: 10.4153/CJM-1992-017-7
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