Abstract We revisit Auslander–Buchweitz approximation theory and find some relations with
cotorsion pairs and model category structures. From the notion of relative generators, we …

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …

Abstract Suppose that T=(A 0 UB) is a formal triangular matrix ring, where A and B are rings
and U is a (B, A)-bimodule. We first study how to construct duality pairs of T-modules using …

We define duality triples and duality pairs in compactly generated triangulated categories
and investigate their properties. This enables us to give an elementary way to determine …

We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

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 …

Let Δ= AANBBMAB be a Morita ring with M⊗ AN= 0= N⊗ BM. We first study how to construct
(complete) duality pairs of Δ-modules using (complete) duality pairs of A-modules and B …

Let X be a class of left R-modules, Y be a class of right R-modules. In this article, we
introduce and study Gorenstein (X, Y)-flat modules as a common generalization of some …

Let $ R $ be a ring with Gwgldim $(R)<\infty $. We obtain a triangle-equivalence $\mathrm
{K}(R\text {-}\mathrm {GProj})\simeq\mathrm {K}(R\text {-}\mathrm {GInj}) $ which restricts to a …

In this paper, we prove that for a $ n $-perfect ring $ R $ various classes of relative
Gorenstein projective $ R $-modules are special precovering, among them including the …