Geodesic
The structure of hereditary rings
Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 139-148 
Yu. A. Drozd. The structure of hereditary rings. Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 139-148. http://geodesic.mathdoc.fr/item/SM_1982_41_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that hereditary rings are isomorphic to rings of triangular matrices with prime blocks along the diagonal. A criterion for triangular rings to be hereditary is given, and when a certain condition (“splitting”) holds it is established that hereditary rings are tensor algebras of special bimodules. Bibliography: 14 titles.

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[2] L. W. Small, “Hereditary rings”, Proc. Nat. Acad. Sci. USA, 55 (1966), 25–27 | DOI | MR | Zbl

[3] A. W. Chatters, “A decomposition theory for Noethenan hereditary rings”, Bull. Londom Math. Soc., 4 (1972), 125–126 | DOI | MR | Zbl

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[6] H. M. Gubareni, O polusovershennykh nasledstvennykh sprava koltsakh modulno-ogranichennogo tipa, Preprint IM-78.1, Kiev, 1978

[7] Yu. A. Drozd, “Stroenie nasledstvennykh kolets”, II Vses. simp. po teorii kolets, algebr i modulei, Kishinev, 1974, 21–22

[8] I. Lambek, Koltsa i moduli, izd-vo “Mir”, Moskva, 1971 | MR

[9] L. A. Koifman, “Koltsa, nad kotorymi singulyarnye moduli in'ektivny. II”, Matem. issledovaniya, 6:3 (1971), 62–84 | MR | Zbl

[10] P. L. Sandomierski, “A note on the global dimension of subrings”, Proc. Amer. Math. Soc., 23 (1969), 478–480 | DOI | MR | Zbl

[11] I. A. Kartan, S. Eilenberg, Gomologicheskaya algebra, IL, Moskva, 1960

[12] H. Bass, “Finitistic dimension and homological generalization of semi-primary rings”, Trans. Amer. Math. Soc., 97 (1960), 367–409 | DOI | MR

[13] D. G. Northcott, An introduction to homological algebra, Univ. Press., Cambridge, 1960 | MR | Zbl

[14] Yu. V. Roganov, “Razmernost tenzornoi algebry proektivnogo bimodulya”, Matem. zametki, 18:6 (1975), 895–902 | MR | Zbl