When are the classes of Gorenstein modules (co)tilting? - Wang, Junpeng; Liu, Zhongkui; Zhao, Renyu (Comptes Rendus. Mathématique)
For the class of Gorenstein projective (resp. injective and flat) modules, we investigate and settle the questions when the middle class is tilting and the other ones are cotilting. The applications have in three directions. The first is to obtain the coincidence between the 1-tilting and silting property, as well as the 1-cotilting and cosilting property of such classes respectively. The second is to characterize Gorenstein modules via finitely generated modules, which provides a proof of that left Noetherian rings with finite left Gorenstein global dimension satisfy First Finitistic Dimension Conjecture and a result related to a question posed by Bazzoni in [J. Algebra 320 (2008) 4281-4299]. The last is to give some new characterizations of Dedekind and Prüfer domains and commutative Gorenstein Artin algebras as well as general (possibly not commutative) Gorenstein rings and Ding–Chen rings.