Stability of Gorenstein categories

Abstract

Abstract. We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective R-modules G = · · ·

$\V\W$-Gorenstein categories

“…Splicing together the split short exact The next relation extends [16,Theorem 4.9] to any category X , and gives a sufficient condition when…”

“…First of all, we investigate the stability of the VW -Gorenstein category under the procedure used to define these entities, which recovers the one defined in [16].…”

“…Let A be an abelian category and W an additive full subcategory of A. Sather-Wagstaff et al introduced in [16] the Gorenstein category G(W), which unifies the following notions: the modules of G -dimension zero [1]; Gorenstein projective and Gorenstein injective modules [6]; V -Gorenstein projective and V -Gorenstein injective modules [8]. The authors proved that G(W) possesses many nice properties under the condition that W is self-orthogonal.…”

“…They play an important role in relative homological algebra. Gorenstein projective and Gorenstein injective modules and some related generalized versions have been studied by many authors; see [1,3,[5][6][7][8][9][10][11][12][13][14][15][16][17] and the literature listed in them.…”

Stability of Gorenstein Flat Modules

“…In [8], Sather-Wagstaff et al investigated the modules that arise from an iteration of the very procedure that leads to the Gorenstein projective modules. Indeed, let P(R) and GP(R) denote the subcategories of projective modules and Gorenstein projective modules, respectively.…”