PRECOVERS AND PREENVELOPES BY MODULES OF FINITE FGT-INJECTIVE AND FGT-FLAT DIMENSIONS

Title & Authors
PRECOVERS AND PREENVELOPES BY MODULES OF FINITE FGT-INJECTIVE AND FGT-FLAT DIMENSIONS
Xiang, Yueming;

Abstract
Let R be a ring and n a fixed non-negative integer. $\small{\cal{TI}_n}$ (resp. $\small{\cal{TF}_n}$) 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 $\small{\prod}$-coherent ring, then every right R-module has a $\small{\cal{TI}_n}$-cover and every left R-module has a $\small{\cal{TF}_n}$-preenvelope. A right R-module M is called n-TI-injective in case $\small{Ext^1}$(N,M) = 0 for any $\small{N\;{\in}\;\cal{TI}_n}$. A left R-module F is said to be n-TI-flat if $\small{Tor_1}$(N, F) = 0 for any $\small{N\;{\in}\;\cal{TI}_n}$. Some properties of n-TI-injective and n-TI-flat modules and their relations with $\small{\cal{TI}_n}$-(pre)covers and $\small{\cal{TF}_n}$-preenvelopes are also studied.
Keywords
$\small{\cal{TI}_n}$-(pre)cover;$\small{\cal{TF}_n}$-preenvelope;n-TI-injective module;n-TI-flat module;weakly n-Gorenstein ring;
Language
English
Cited by
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