An n-FC ring is a left and right coherent ring whose left and right self-FP-injective dimension
is n. The work of Ding and Chen shows that these rings possess properties which generalize …

We characterize Ding modules and complexes over Ding-Chen rings. We show that, over a
Ding-Chen ring R, the Ding projective (respectively, Ding injective, respectively, Ding flat) R …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

We give necessary and sufficient conditions in order for the class of projectively coresolved
Gorenstein flat modules, PGF (respectively that of projectively coresolved Gorenstein B flat …

An R-module M is called Ding projective if there exists an exact sequence⋯→ P1→ P0→
P0→ P1→⋯ of projective R-modules with M= Ker (P0→ P1) such that Hom (-, F) leaves the …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

Let $ T=\biggl (\begin {matrix} A&0\\U&B\end {matrix}\biggr) $ be a formal triangular matrix
ring, where $ A $ and $ B $ are rings and $ U $ is a $(B, A) $-bimodule. We prove that:(1) If …

Let 𝒜 be an abelian category having enough projective and injective objects, and let 𝒯 be
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …

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 …

Let X be a class of right R-modules that contains all projective right R-modules. The notion of
X-Gorenstein projective modules was introduced by D. Bennis and K. Ouarghi (X-Gorenstein …