[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2010.25.4.497

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

Xiang, Yueming (COLLEGE OF MATHEMATICS AND COMPUTER SCIENCE HUNAN NORMAL UNIVERSITY)

Publication Information

Communications of the Korean Mathematical Society / v.25, no.4, 2010 , pp. 497-510 More about this Journal

Abstract

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

Keywords

$\cal{TI}_n$ -(pre)cover; $\cal{TF}_n$ -preenvelope; n-TI-injective module; n-TI-flat module; weakly n-Gorenstein ring;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)
Times Cited By SCOPUS : 0

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