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Relative Cohomology

Published online by Cambridge University Press:  20 November 2018

D. G. Higman
D. G. Higman*
Affiliation:
Montana State University and University of Michigan
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It is our purpose in this paper to present certain aspects of a cohomology theory of a ring R relative to a subring S, basing the theory on the notions of induced and produced pairs of our earlier paper (2), but making the paper self-contained except for references to a few specific results of (2). The cohomology groups introduced occur in dual pairs. Generic cocycles are defined, and the groups are related to the protractions and retractions of R-modules.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 19 - 34
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Cartan, H. and Eilenberg, S., Homological algebra (Princeton, 1956).Google Scholar
2. Higman, D. G., Induced and produced modules, Can. J. Math., 7 (1955), 490–508.Google Scholar
3. Higman, D. G., On orders in separable algebras, Can. J. Math., 7 (1955), 509–515.Google Scholar
4. Higman, D. G., On representations of orders (in preparation).Google Scholar
5. Hochschild, G., On the cohomology theory for associative algebras, Ann. Math., 46 (1945), 58–67.Google Scholar
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