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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
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