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 …

To a big-tilting object in a complete, cocomplete abelian category with an injective
cogenerator we assign a big-cotilting object in a complete, cocomplete abelian category with …

A full subcategory of a Grothendieck category is called deconstructible if it consists of all
transfinite extensions of some set of objects. This concept provides a handy framework for …

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the
Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler …

Let $ R $ be a ring and $\mathsf S $ be a class of strongly finitely presented (FP ${} _\infty $)
$ R $-modules closed under extensions, direct summands, and syzygies. Let $(\mathsf …

Mittag-Leffler modules occur naturally in algebra, algebraic geometry, and model
theory,[20],[14],[19]. If R is a non-right perfect ring, then it is known that in contrast with the …

We present a general construction of model category structures on the category C (Qco (X))
of unbounded chain complexes of quasi-coherent sheaves on a semi-separated scheme X …

In this article, we provide several descriptions of w-coherent rings in terms of modules. We
show that a ring R is w-coherent if and only if every direct product of flat modules is w-flat. To …

A classic result by Bass says that the class of all projective modules is covering if and only if
it is closed under direct limits. Enochs extended the if-part by showing that every class of …

Baer's Criterion of injectivity implies that injectivity of a module is a factorization property with
respect to\a single monomorphism. Using the notion of a cotorsion pair, we study …