Formula omitted]-Gorenstein modules

Abstract

Let W be a self-orthogonal class of left R-modules. We introduce and study W -Gorenstein modules as a common generalization of some known modules such as Gorenstein projective (injective) modules (Enochs and Jenda, 1995 [7]) and V-Gorenstein projective (injective) modules (Enochs et al., 2005 [12]). Special attention is paid to W P -Gorenstein and W I -Gorenstein modules, where W P = { C ⊗ R P | P is a projective left R -module } and W I = { Hom S ( C , E ) | E is an injective left S -module } with C R S a faithfully semidualizing bimodule.