Note on Relative Homological Dimension

G. Hochschild
1958 Nagoya mathematical journal  
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 [4], we have defined the relative analoguesof the functorsof Cartan-Eilenberg [1], and we have briefly treated the corresponding relative analogues of module dimension and global ring dimension.
doi:10.1017/s0027763000023539 fatcat:z66haesrkjdqzbdjjx7ndewuqm