On rings with finite Gorenstein weak global dimension

Abstract

Let [Formula: see text] be a ring with finite Gorenstein weak global dimension. We characterize Gorenstein projective, injective and flat modules over [Formula: see text]. As an application, it is proved that [Formula: see text] is (strongly) CM-free if and only if [Formula: see text] has finite weak global dimension.

Gorenstein $\mathrm{FP}_n$-flat modules and weak global dimensions

“…Note that in the sense of Definition 3.5 a Gorenstein ring is precisely a Gorenstein 0-coherent ring, and a Gorenstein 1-coherent ring is precisely a Ding-Chen ring [8]. Thus, the previous result recovers and extends the known in [18,Lemma 1.2].…”