PRECOVERS AND PREENVELOPES BY MODULES OF FINITE FGT-INJECTIVE AND FGT-FLAT DIMENSIONS Xiang, Yueming;
Let R be a ring and n a fixed non-negative integer. (resp. ) denotes the class of all right R-modules of FGT-injective dimensions at most n (resp. all left R-modules of FGT-flat dimensions at most n). We prove that, if R is a right -coherent ring, then every right R-module has a -cover and every left R-module has a -preenvelope. A right R-module M is called n-TI-injective in case (N,M) = 0 for any . A left R-module F is said to be n-TI-flat if (N, F) = 0 for any . Some properties of n-TI-injective and n-TI-flat modules and their relations with -(pre)covers and -preenvelopes are also studied.