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 …

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 …

We prove that, for any n≥ 2, the classes of FP n-injective modules and of FP n-flat modules
are both covering and preenveloping over any ring R. This includes the case of FP∞ …

Let R be a commutative ring. We show that any complete duality pair gives rise to a theory of
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …

In the derived category of a commutative noetherian ring, we explicitly construct a silting
object associated with each sp-filtration of the Zariski spectrum satisfying the “slice” …

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 …

In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …

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 …

Gorenstein injective covers and envelopes over noetherian rings Page 1 PROCEEDINGS OF
THE AMERICAN MATHEMATICAL SOCIETY Volume 143, Number 1, January 2015, Pages …