ABSTRACT
The work of Ding, Mao, and Li provides a natural way to extend notions from Gorenstein homological algebra from noetherian to coherent rings. In the process, the Gorenstein modules are replaced by Ding modules. Like the Gorenstein projectives, the Ding projective modules are also cycles of exact complexes of projective modules. While the Gorenstein modules have very nice properties over Gorenstein rings, the Ding modules have nice properties over the so-called Ding-Chen rings. A Ding-Chen ring is a coherent ring R (i.e., left and right coherent) which has finite absolutely pure (i.e., FP-injective) dimension as both a left and right module over itself. The chapter also proves that over a Ding-Chen ring the complete cotorsion pair (W, DI) is actually a perfect cotorsion pair, and therefore that the class DI is enveloping.
