TY - JOUR T1 - On $G$-$(n,d)$-rings and $n$-coherent rings AU - Li, Weiqing PY - 2025 DA - January DO - 10.24330/ieja.1502064 JF - International Electronic Journal of Algebra JO - IEJA PB - Abdullah HARMANCI WT - DergiPark SN - 1306-6048 SP - 147 EP - 178 VL - 37 IS - 37 LA - en AB - 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 $d \leq n$. 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. 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