Geodesic
Layer-projective lattices. I
Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 170-182

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The class of layer-projective lattices is singled out. For example, it contains the lattices of subgroups of finite Abelian $p$-groups, finite modular lattices of centralizers that are indecomposable into a finite sum, and lattices of subspaces of a finite-dimensional linear space over a finite field that are invariant with respect to a linear operator with zero eigenvalues. In the class of layer-projective lattices, the notion of type (of a lattice) is naturally introduced and the isomorphism problem for lattices of the same type is posed. This problem is positively solved for some special types of layer-projective lattices. The main method is the layer-wise lifting of the coordinates. 
@article{MZM_1998_63_2_a1,
     author = {V. A. Antonov and Yu. A. Nazyrova},
     title = {Layer-projective lattices. {I}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {170--182},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a1/}
}
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V. A. Antonov; Yu. A. Nazyrova. Layer-projective lattices. I. Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 170-182. http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a1/