• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.31-47
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• 2012

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 at 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 at and Ding injective dimensions of modules together with Ding injective precovers. We then discuss balance of functors Hom and tensor.