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On Hereditary and Cohereditary Modules

Published online by Cambridge University Press:  20 November 2018

M. S. Shrikhande
M. S. Shrikhande*
Affiliation:
University of Wisconsin, Madison, Wisconsin; University of Wyoming, Laramie, Wyoming
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 892 - 896
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Azumaya, G., M-projective and M-injective modules (to appear).Google Scholar
2. Beachy, J., Bicommutators of cofaithful, fully divisible modules, Can. J. Math. 23 (1971), 202–213.Google Scholar
3. Cartan, H., and Eilenberg, S., Homological algebra (Princeton University Press, Princeton, 1956).Google Scholar
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5. Lambek, J., Lectures on rings and modules (Blaisdell, Waltham, Mass., 1966).Google Scholar
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