PRECOVERS AND PREENVELOPES BY MODULES OF FINITE FGT-INJECTIVE AND FGT-FLAT DIMENSIONS
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Let R be a ring and n a fixed non-negative integer. T In (resp. T Fn) 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 Rmodule has a T In-cover and every left R-module has a T Fn-preenvelope. A right R-module M is called n-TI-injective in case Ext1(N,M) = 0 for any N ε T In. A left R-module F is said to be n-TI-flat if Tor1(N, F) =0 for any N 2 T In. Some properties of n-TI-injective and n-TI-flat modules and their relations with T In-(pre)covers and T Fn-preenvelopes are also studied.
Abstract
Let R be a ring and n a fixed non-negative integer. T In (resp. T Fn) 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 Rmodule has a T In-cover and every left R-module has a T Fn-preenvelope. A right R-module M is called n-TI-injective in case Ext1(N,M) = 0 for any N ε T In. A left R-module F is said to be n-TI-flat if Tor1(N, F) =0 for any N 2 T In. Some properties of n-TI-injective and n-TI-flat modules and their relations with T In-(pre)covers and T Fn-preenvelopes are also studied.
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