Homological invariants related to semidualizing bimodules
Volume 156 / 2019
Abstract
\looseness -1Let and S be rings and _RC_S a semidualizing bimodule. We show that the supremum of the C-projective dimensions of C-flat left R-modules is less than or equal to that for left R-modules with finite C-projective dimension, and the latter is less than or equal to the supremum of the C-injective dimensions of projective (or flat) left S-modules. We also show that the supremum of the C-projective dimensions of injective left R-modules and that of the C-injective dimensions of projective left S-modules are identical provided that both of them are finite. Finally, we show that the supremum of the C-projective dimensions of C-flat left R-modules (a relative homological invariant) and that of the projective dimensions of flat left S-modules (an absolute homological invariant) coincide.
