Geodesic
Noncommutative valuation rings in simple finite-dimensional algebras over a field
Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 493-505 
N. I. Dubrovin. Noncommutative valuation rings in simple finite-dimensional algebras over a field. Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 493-505. http://geodesic.mathdoc.fr/item/SM_1985_51_2_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper studies rings in simple finite-dimensional algebras over a field that are similar to valuation rings in fields. Bibliography: 15 titles.

[1] Dubrovin N. I., “Nekommutativnye koltsa normirovaniya”, Trudy MMO, 45 (1982), 265–280 | MR | Zbl

[2] Kherstein I., Nekommutativnye koltsa, Mir, M., 1972 | MR

[3] Burbaki N., Kommutativnaya algebra, Mir, M., 1971 | MR

[4] Dubrovin N. I., “Koltsa normirovaniya v prostoi konechnomernoi algebre nad polem”, UMN, 33:3 (1978), 167 | MR | Zbl

[5] Pyatyi Vsesoyuznyi simpozium po teorii kolets, algebr i modulei, Novosibirsk, 1982

[6] Kon Ya., Svobodnye koltsa i ikh svyazi, Mir, M., 1975 | MR

[7] Dubrovin N. I., “Tsepnye oblasti”, Vestn. MGU. Seriya matem., mekh., 1980, no. 2, 51–54 | MR | Zbl

[8] Feis K., Algebra: koltsa, moduli i kategorii, Ch. 1, Mir, M., 1977

[9] Dubrovin N. I., “Maksimalnye poryadki v prostoi tsentralnoi konechnomernoi algebre nad koltsom normirovaniya vysoty 1”, Matem. sb., 108(150) (1979), 518–528 | MR

[10] Schilling O. F. G., “The theory of valuations”, Math. Surveyes, 4, Amer. Math. Soc., Providence, RI, 1950, MR13,315b | MR

[11] Jacobson N., PI-algebras, Lecture notes in math., 441 | MR | Zbl

[12] Kokorin A. I., Kopytov V. M., Lineino uporyadochennye gruppy, Nauka, M., 1972 | MR | Zbl

[13] Meyer F., Inyraham E., Separable algebras over commutative rings, Lecture notes in math., 181, 1971

[14] Dubrovin N. I., “O koltsakh glavnykh pravykh idealov”, Izv. VUZov, 1981, no. 2, 30–37 | MR | Zbl

[15] Leng S., Algebra, Mir, M., 1968