Geodesic
Representations of partially ordered sets over commutative rings
Izvestiya. Mathematics, Tome 10 (1976) no. 3, pp. 497-514 
V. V. Plakhotnik. Representations of partially ordered sets over commutative rings. Izvestiya. Mathematics, Tome 10 (1976) no. 3, pp. 497-514. http://geodesic.mathdoc.fr/item/IM2_1976_10_3_a3/
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     title = {Representations of partially ordered sets over commutative rings},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this work a criterion is given for the finiteness of the number of indecomposable representations of partially ordered sets over an arbitrary commutative ring. Determination of finiteness is reduced to solving a matrix problem. Bibliography: 8 titles.

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[2] Gabriel P., “Unzerlegbare Darstellungen. I”, Manuscripta Math., 6 (1972), 71–103 | DOI | MR | Zbl

[3] Nazarova L. A., “Predstavleniya kolchanov beskonechnogo tipa”, Izv. AN SSSR. Ser. matem., 37 (1973), 752–791 | MR | Zbl

[4] Kleiner M. M., “Chastichno uporyadochennye mnozhestva konechnogo tipa”, Zapiski nauchnykh seminarov LOMI, 28, 1972, 32–41 | MR | Zbl

[5] Kleiner M. M., “O tochnykh predstavleniyakh chastichno uporyadochennykh mnozhestv konechnogo tipa”, Zapiski nauchnykh seminarov LOMI, 28, 1972, 42–59 | MR

[6] Berman S. D., Zhilinskaya Z. P., “O sovmestnykh pryamykh razlozheniyakh konechnoporozhdennoi abelevoi gruppy i ee podgruppy”, Dokl. AN SSSR, 210:5 (1973), 5–8

[7] Atya M., Makdonald I., Vvedenie v kommutativnuyu algebru, Mir, M., 1972, 111–112 | MR

[8] Drozd Yu. A., “Matrichnye zadachi i kategorii matrits”, Zapiski nauchnykh seminarov LOMI, 28, 1972, 114–153 | MR | Zbl