We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose …

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 …

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 …

K-flatness for unbounded complexes of modules over a ring R was introduced by
Spaltenstein [27], as an analogue of the classical notion of flatness for modules. In this …

Balanced pairs appear naturally in the realm of relative homological algebra associated with
the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural …

The existence of the Gorenstein projective precovers over arbitrary rings is an open
question. It is known that if the ring has finite Gorenstein global dimension, then every …

Let (G,⊗) be any closed symmetric monoidal Grothendieck category. We show that K-flat
covers exist universally in the category of chain complexes and that the Verdier quotient of K …

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 …

We prove that Vopěnka's Principle implies that for every class X of modules over any ring,
the class of X-Gorenstein Projective modules (X-GP) is a precovering class. In particular, it is …