We study the behaviour of modules M that fit into a short exact sequence 0→ M→ C→ M→ 0,
where C belongs to a class of modules CC, the so-called C C-periodic modules. We find a …

Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

In this paper, we examine the class of K-absolutely pure complexes. These are the
complexes which are right orthogonal in the homotopy category K (R) to the acyclic …

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 …

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 …

Let R be a ring and X a chain complex of R-modules. It is proven that if each term X_i X i is
Ding injective in R-Mod for all i ∈ Z i∈ Z, and there exists an integer k such that each Z _iX …

Let R be any ring with identity. We show that the homotopy category of all acyclic chain
complexes of pure-projective R-modules is a compactly generated triangulated category …

We introduce a notion of pure-minimality for chain complexes of modules and show that it
coincides with (homotopic) minimality in standard settings, while being a more useful notion …

Krause [19] has proved that the homotopy category K (R-PureProj) of pure projective
modules over an associative ring R is compactly generated and equivalent to the Verdier …

Let RR be a ring with identity. Inspired by recent work in Emmanouil, Preprint, 2021, we
show that the derived category of RR is equivalent to the chain homotopy category of all K …