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- W2075821228 abstract "Let R be a ring and n a fixed non-negative integer. <TEX>$cal{TI}_n$</TEX> (resp. <TEX>$cal{TF}_n$</TEX>) 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 <TEX>$prod$</TEX>-coherent ring, then every right R-module has a <TEX>$cal{TI}_n$</TEX>-cover and every left R-module has a <TEX>$cal{TF}_n$</TEX>-preenvelope. A right R-module M is called n-TI-injective in case <TEX>$Ext^1$</TEX>(N,M) = 0 for any <TEX>$N;{in};cal{TI}_n$</TEX>. A left R-module F is said to be n-TI-flat if <TEX>$Tor_1$</TEX>(N, F) = 0 for any <TEX>$N;{in};cal{TI}_n$</TEX>. Some properties of n-TI-injective and n-TI-flat modules and their relations with <TEX>$cal{TI}_n$</TEX>-(pre)covers and <TEX>$cal{TF}_n$</TEX>-preenvelopes are also studied." @default.
- W2075821228 created "2016-06-24" @default.
- W2075821228 creator A5078583781 @default.
- W2075821228 date "2010-10-31" @default.
- W2075821228 modified "2023-09-26" @default.
- W2075821228 title "PRECOVERS AND PREENVELOPES BY MODULES OF FINITE FGT-INJECTIVE AND FGT-FLAT DIMENSIONS" @default.
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- W2075821228 doi "https://doi.org/10.4134/ckms.2010.25.4.497" @default.
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