In this paper we study the finiteness of global Gorenstein AC-homological dimensions for
rings, and answer the questions posed by Becerril, Mendoza, Pérez and Santiago. As an …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

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 …

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states
that “for what rings R do we have K (AC)= K (R-Inj)?”. We give an answer to such a question …

In this paper we develop the homological properties of the $(\mathcal {L},\mathcal {A}) $-
Gorenstein flat $ R $-modules $\mathcal {GF} _ {(\mathcal {F}(R),\mathcal {A})} $ proposed …

From the notion of (co) generator in relative homological algebra, we present the concept of
finite balanced system $[(\mathcal {X},\omega);(\nu,\mathcal {Y})] $ as a tool to induce …

We present the concept of cotorsion pairs cut along subcategories of an abelian category.
This provides a generalization of complete cotorsion pairs, and represents a general …

Let A and B be rings and U a (B, A)-bimodule. If BU is flat and UA is finitely generated
projective (resp., BU is finitely generated projective and UA is flat), then the characterizations …

In this paper, the relative derived categories with respect to X-Gorenstein projective modules
and Y-Gorenstein injective modules are introduced to unify Gorestein derived categories …