Geodesic
Multiplicative functions of locally finite partially ordered sets. Multiplicativity criteria
Matematičeskie zametki, Tome 47 (1990) no. 1, pp. 105-114.

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@article{MZM_1990_47_1_a10,
     author = {E. E. Marenich},
     title = {Multiplicative functions of locally finite partially ordered sets. {Multiplicativity} criteria},
     journal = {Matemati\v{c}eskie zametki},
     pages = {105--114},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1990_47_1_a10/}
}
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E. E. Marenich. Multiplicative functions of locally finite partially ordered sets. Multiplicativity criteria. Matematičeskie zametki, Tome 47 (1990) no. 1, pp. 105-114. http://geodesic.mathdoc.fr/item/MZM_1990_47_1_a10/