Relative Cohomology

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Abstract
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.

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