ON G- ( n, d )-RINGS AND n-COHERENT RINGS

. Let n and d be non-negative integers. We introduce the concept of strongly (n, d)-injective modules to characterize n-coherent rings. For a right perfect ring R, it is shown that R is right n-coherent if and only if every right R-module has a strongly (n, d)-injective (pre)cover for some non-negative integer d <= n. We also provide equivalent conditions for an (n, d)-ring being n-coherent. Then we investigate the so-called right G-(n, d)-rings, over which every n-presented right module has Gorenstein projective dimension at most d. Finally, we prove a Gorenstein analogue of Costa's first conjecture.