Geodesic
Number of equivalence classes of weakly equivalent lattices
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 501-508.

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Two complete lattices, $M$ and $N$, lying in an algebra over the field of rational numbers, are said to be weakly left equivalent if $N=KM$ and $M=\overline KN$, where $K$ is a two-sided invertible lattice and $\overline K$ is the inverse for $K$. In this paper we prove that the number of equivalence classes of lattices contained in a weak equivalence class is finite. 
@article{MZM_1974_15_3_a16,
     author = {I. A. Levina},
     title = {Number of equivalence classes of weakly equivalent lattices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {501--508},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a16/}
}
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I. A. Levina. Number of equivalence classes of weakly equivalent lattices. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 501-508. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a16/