This is the second revised edition of an introduction to contemporary relative homological
algebra. It supplies important material essential to understand topics in algebra, algebraic …

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 …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

Our aim is to give a fairly complete account on the construction of compatible model
structures on exact categories and symmetric monoidal exact categories, in some cases …

Hereditary abelian model categories | Bulletin of the London Mathematical Society | Oxford
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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 …

An R-module M is called Ding projective if there exists an exact sequence⋯→ P1→ P0→
P0→ P1→⋯ of projective R-modules with M= Ker (P0→ P1) such that Hom (-, F) leaves the …

We show that if the given cotorsion pair in the category of modules is complete and
hereditary, then both of the induced cotorsion pairs in the category of complexes are …

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 …

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …