On the <i>C</i> -flat dimension of injective modules

Abstract Let R and S be rings and let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mmultiscripts> <m:mi>C</m:mi> <m:mi>S</m:mi> <m:none/> <m:mprescripts/> <m:mi>R</m:mi> <m:none/> </m:mmultiscripts> </m:math> {{}_{R}C_{S}} be a semidualizing bimodule. We investigate the behavior of the C -flat dimension of injective left R -modules, and establish the relation among the supremum of these C -flat dimensions and the supremum of C -injective dimensions of projective left S -modules and the supremum of C -projective dimensions of injective left R -modules.