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LetRbe a ring with identity element 1, and letSbe a subring ofRcontaining 1. We considerR-modules on which 1 acts as the identity map, and we shall simultaneously regard suchR-modules asS-modules in the natural way. In , we have defined the relative analoguesof the functorsof Cartan-Eilenberg , and we have briefly treated the corresponding relative analogues of module dimension and global ring dimension.doi:10.1017/s0027763000023539 fatcat:z66haesrkjdqzbdjjx7ndewuqm