Geodesic
On Hereditary and Cohereditary Modules
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 892-896

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

A recent paper by Goro Azumaya on M-projective and M-injective modules [1] suggests a generalization of the concept of hereditary rings to modules which is also capable of dualization. Section 2 is devoted to preliminaries on M-projective and M-infective modules.In section 3, we introduce the notion of hereditary and cohereditary modules. An R-module is called hereditary if every R-submodule of it is projective. Cohereditary modules are defined dually. 
Shrikhande, M. S. On Hereditary and Cohereditary Modules. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 892-896. doi: 10.4153/CJM-1973-094-2
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[1] 1. Azumaya, G., M-projective and M-injective modules (to appear). Google Scholar

[2] 2. Beachy, J., Bicommutators of cofaithful, fully divisible modules, Can. J. Math. 23 (1971), 202–213. Google Scholar

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

[4] 4. Faith, C., Lectures on injective modules and quotient rings, No. J+9 (Springer-Verlag, Berlin- Heidelberg, N.Y., 1967). Google Scholar

[5] 5. Lambek, J., Lectures on rings and modules (Blaisdell, Waltham, Mass., 1966). Google Scholar

[6] 6. Rosenberg, A., and Zelinsky, D., On the finiteness of the injective hull, Math. Z. 70 (1959), 372–380. Google Scholar

[7] 7. Vamos, P., The dual of the notion of “finitely generated”, J. London Math. Soc. J+3 (1968), 643–646. Google Scholar

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