Note on Relative Homological Dimension

Let R be a ring with identity element 1, and let S be a subring of R containing 1. We consider R-modules on which 1 acts as the identity map, and we shall simultaneously regard such R-modules as S-modules in the natural way. In [4], we have defined the relative analogues of the functors of Cartan-Eilenberg [1], and we have briefly treated the corresponding relative analogues of module dimension and global ring dimension.