Journal of the
Korean Mathematical Society JKMS

The so-called Ding-Chen ring is an $n$-FC ring which is both left and right coherent, and has both left and right self FP-injective dimensions at most $n$ for some non-negative integer $n$. In this paper, we investigate the classes of the so-called Ding projective, Ding injective and Gorenstein flat modules and show that some homological properties of modules over Gorenstein rings can be generalized to the modules over Ding-Chen rings. We first consider Gorenstein flat and Ding injective dimensions of modules together with Ding injective precovers. We then discuss balance of functors $\text{Hom}$ and tensor.

Keywords: Ding-Chen ring, Ding projective and Ding injective module, Gorenstein flat module, precover, preenvelope, balanced functors

MSC numbers: 16E05, 16E65, 18G20, 18G25