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 $ext{Hom}$ and tensor.
展开▼
机译：所谓的Ding-Chen环是一个$ n $ -FC环，它左右相干，并且对于一些非负整数$ n $而言，左右FP自我注入维数最多为$ n $。在本文中，我们研究了所谓的Ding射影，Ding内射模和Gorenstein平板模块的类，并表明可以将Gorenstein环上的模块的某些同源性推广到Ding-Chen环上的模块。我们首先考虑Gorenstein平面和Ding内射模量以及Ding内射前盖。然后，我们讨论函子$ text {Hom} $和张量的平衡。
展开▼
