X-GORENSTEIN PROJECTIVE AND Y-GORENSTEIN INJECTIVE MODULES

Authors : Fanyun MENG, Qunxing PAN

Pages : 537-554

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Publication Date : 2011-04-01

Article Type : Research Paper

Abstract :Let X be a class of right R-modules that contains all projective right R-modules. The notion of X-Gorenstein projective modules was introduced by D. Bennis and K. Ouarghi insert ignore into journalissuearticles values(X-Gorenstein projective modules, International Mathematical Forum 5 insert ignore into journalissuearticles values(10);, 487–491, 2010);. In this paper, we introduce Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules, where Y is a class of right R-modules that contains all injective right R-modules. We show that the principal results on Gorenstein modules remain true for X-Gorenstein projective right R-modules, Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules.
Keywords : X Gorenstein projective modules, Y Gorenstein injective modules, Y Gorenstein flat modules, 2000 AMS Classification 16 E 10