References
Bass, H.: Finitistic dimension and a homological generalization of semi-primary rings. Trans. Amer. Math. Soc.95, 466–488 (1960).
Cohen, I. S., Kaplansky, I.: Rings for which every module is a direct sum of cyclic modules. Math. Z.54, 97–101 (1951).
Faith, C.: On Köthe rings. Math. Ann.164, 207–212 (1966).
-- Walker, E. A.: Direct sum representations of injective modules. J. of Algebra.
Griffith, P.: A note on a theorem of Hill. Pacific J. Math. to appear.
Heller, A., Reiner, I.: Indecomposable representations. III. J. Math.5, 314–323 (1961).
Ikeda, M.: A characterization of quasi-Frobenius rings. Osaka Math. J.4, 203–210 (1952).
Jans, J. P.: Rings and homology. New York: Holt, Rinehart and Winston, 1964.
Kaplansky, I.: Projective modules. Ann. of Math.68, 371–377 (1958).
Köthe, G.: Verallgemeinerte Abelsche Gruppen mit hyperkomplexen Operatorenringen. Math. Z.39, 31–44 (1934).
Mac Lane, S.: Homology. Berlin-Göttingen-Heidelberg: Springer 1963.
Nakayama, T.: On Frobennisean algebras II. Ann. of Math.42, 1–21 (1941).
—— Note on uni-serial and generalized uniserial rings. Proc. Imp. Acad. Tokyo16, 285–289 (1940).
Warfield, R. B.: Purity and algebraic compactness for modules. To appear.
-- Decompositions of injective modules. To appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Griffith, P. On the decomposition of modules and generalized left uniserial rings. Math. Ann. 184, 300–308 (1970). https://doi.org/10.1007/BF01350858
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01350858