Geodesic
Modules lattice isomorphic to linearly compact modules
Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 174-181 
G. M. Brodskii. Modules lattice isomorphic to linearly compact modules. Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 174-181. http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a2/
@article{MZM_1996_59_2_a2,
     author = {G. M. Brodskii},
     title = {Modules lattice isomorphic to linearly compact modules},
     journal = {Matemati\v{c}eskie zametki},
     pages = {174--181},
     year = {1996},
     volume = {59},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study modules that are lattice isomorphic to linearly compact modules (in the discrete topology). In particular, we establish the equivalence of the following properties of a module $M$: 1) $M$ satisfies the Grothendieck property \textrm{AB$5^*$} and all its submodules are Goldie finite-dimensional; 2) $M$ is lattice isomorphic to a linearly compact module; 3) $M$ is lattice antiisomorphic to a linearly compact module. We show that a linearly compact module cannot be determined in terms of the lattice of its submodules.

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