Geodesic
The Classification of Algebras by Dominant Dimension
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 398-409

Voir la notice de l'article provenant de la source Cambridge University Press

Nakayama proposed to classify finite-dimensional algebras R over a field according to how long an exact sequence of projective and injective R-R-bimodules Xi they allow. He conjectured that if there exists an infinite sequence of this type, then R must be quasi-Frobenius; and he proved this when R is generalized uniserial (17). 
Mueller, Bruno J. The Classification of Algebras by Dominant Dimension. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 398-409. doi: 10.4153/CJM-1968-037-9
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[1] 1. Bass, H., Infective dimension in Noetherian rings, Trans. Amer. Math. Soc, 102 (1962), 18–29. Google Scholar

[2] 2. Bourbaki, N., Elements de mathématique-. Algèbre (Paris, 1958), Chap. 8. Google Scholar

[3] 3. Cartan, H. and Eilenberg, S., Homologuai algebra (Princeton, 1956). Google Scholar

[4] 4. Curtis, C. W. and Jans, J. P., On algebras with a finite number of indecomposable modules, Trans. Amer. Math. Soc, 114 (1965), 122–132. Google Scholar

[5] 5. Eckmann, B. und Schopf, A., Tiber injektive Moduln, Arch. Math., 4 (1953), 75–78. Google Scholar

[6] 6. Eilenberg, S., Nagao, N., and Nakayama, T., On the dimension of modules and algebras IV, Nagoya Math. J., 10 (1956), 87–95. Google Scholar

[7] 7. Jans, J. P., Projective infective modules, Pacific J. Math., 9 (1959), 1103–1108. Google Scholar

[8] 8. Jans, J. P., Some generalizations of finite projective dimension, Illinois J. Math., 5 (1961), 334–344. Google Scholar

[9] 9. Kupisch, H., Symmetrische Algebren mit endlich vielen unzerlegbaren Darstellungen I, J. Reine Angew. Math., 219 (1965), 1–25. Google Scholar

[10] 10. Matlis, E., Injective modules over Noetherian rings, Pacific J. Math., 8 (1958), 511–528. Google Scholar

[11] 11. Mochizuki, H. Y., Finitistic global dimension for rings, Pacific J. Math., 15 (1965), 249–258. Google Scholar

[12] 12. Mochizuki, H. Y., On the double commutator algebra of QF-3 algebras, Nagoya Math. J., 25 (1965), 221–230. Google Scholar

[13] 13. Morita, K., Duality for modules and its applications to the theory of rings with minimum condition, Sci. Repts. Tokyo Kyoiku Daigaku, Sect. A, 6 (1958), 83–142. Google Scholar

[14] 14. Morita, K., On algebras for which every faithful representation is its own second commutator, Math. Z., 69 (1958), 429–434. Google Scholar

[15] 15. Morita, K., Category-isomorphisms and endomorphism rings of modules, Trans. Amer. Math. Soc, 108 (1962), 451–469. Google Scholar

[16] 16. Nakayama, T., On Frobeniusean algebras II, Ann. of Math., J$ (1941), 1–21.10.2307/1968984 Google Scholar | DOI

[17] 17. Nakayama, T., On algebras with complete homology, Abh. Math. Sem. Univ. Hamburg, 22 (1958), 300–307. Google Scholar

[18] 18. Tachikawa, H., A characterization of QF-3 algebras, Proc Amer. Math. Soc, 13 (1962), 701–703; 14 (1963), 995. Google Scholar

[19] 19. Tachikawa, H., Qn dominant dimension of QF-3 algebras, Trans. Amer. Math. Soc, 112 (1964), 249–266. Google Scholar

[20] 20. Thrall, R. M., Some generalizations of quasi-Frobenius algebras, Trans. Amer. Math. Soc, 64 (1948), 173–183. Google Scholar

[21] 21. Wall, D. W., Algebras with unique minimal faithful representations, Duke Math. J., 25 1958), 321–329. Google Scholar

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