Geodesic
A Characterization of Sharply Transferable Lattices
Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 145-154

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

A lattice L is called transferable if and only if, whenever L can be embedded in the ideal lattice I(K) of a lattice K, L can be embedded in K. L is called sharply transferable if and only if, for every lattice embedding ψ(x) , there exists an embedding such that for x, y ε L, if and only if x ≤ y. Finite sharply transferable lattices were characterized in [3]. In this paper we extend the characterization to the infinite case. We begin by revising some of the terminology of [3].1.1. Definition, (a) Let 〈P; ≧〉 be a poset and X, Y ⊆ P. Then X dominates Y (written X Dom Y) if and only if, for every y ∈ F, there exists x ∈ X such that y ∈ x. Dually, X supports Y (written X Spp Y) if and only if, for every y ∈ Y, there exists x ∈ X such that x ≦ y. 
Grätzer, G.; Platt, C. R. A Characterization of Sharply Transferable Lattices. Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 145-154. doi: 10.4153/CJM-1980-011-8
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