Geodesic
Sublattices of Modular Lattices of Finite Length
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 95-98

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It is well-known that the join-irreducible elements J(L) and the meet-irreducible elements M(L) of a lattice L of finite length play a central role in its arithmetic and, especially, in the case that L is distributive. In [3] it was shown that the quotient set Q(L) = {b/a | a ∊ J(L), b ∊ M(L), a ≤ b} plays a somewhat analogous role in the study of the sublattices of L. Indeed, in a lattice L of finite length, if S is a sublattice of L then S = L — ∪b/a∊A [a, b] for some A ⊆ Q(L). Furthermore, the converse actually characterizes finite distributive lattices [3]. 
Rival, Ivan. Sublattices of Modular Lattices of Finite Length. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 95-98. doi: 10.4153/CMB-1975-017-6
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     title = {Sublattices of {Modular} {Lattices} of {Finite} {Length}},
     journal = {Canadian mathematical bulletin},
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     year = {1975},
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     doi = {10.4153/CMB-1975-017-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-017-6/}
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