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 …

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …

Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …

Let R be a ring and X a chain complex of R-modules. It is proven that if each term X_i X i is
Ding injective in R-Mod for all i ∈ Z i∈ Z, and there exists an integer k such that each Z _iX …

A complex X is called Ding injective if there exists an exact sequence of injective
complexes…→ E 1→ E 0→ E-1→… such that X= K er (E 0→ E-1), and the sequence …

Let R be a ring (not necessarily commutative) and (ℒ, 𝒜) a bi-complete duality pair. We
investigate the notions of (flat-typed)(ℒ, 𝒜)-Gorenstein rings, which unify Iwanaga …

In this paper, we generalize the idea of Song, Zhao and Huang [Czechoslov. Math. J., 70,
483–504 (2020)] and introduce the notion of right (left) Gorenstein subcategory\(r {\cal …

For an integer N≥ 2 and three subcategories 𝒲, 𝒳, 𝒴 of modules, we study the notion of (𝒲,
𝒳, 𝒴)-Gorenstein N-complexes. We show that under certain hypotheses, an N-complex C is …

设R 是交换环, C 是一个半对偶R-模, X 是一个R-模类. 引入了X-GC-投射复形的概念,
证明了复形M 是XG C-投射的当且仅当M 的每个层次上的模都是XG C-投射模, 并且对任意的CX …

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective
modules over an Iwanaga-Gorenstein ring, we present the concept of left and right n …