For a left coherent ring A with every left ideal having a countable set of generators, we show
that the coderived category of left A-modules is compactly generated by the bounded …

We prove that, if GProj is the class of all Gorenstein projective modules over a ring R, then
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …

Let $ R $ be the quotient of a regular coherent commutative ring by a finitely generated
ideal. In this paper, we classify all abelian subcategories of finitely presented $ R $-modules …

We study the notions of n-hereditary rings and its connection to the classes of finitely n-
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …

For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S− and
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …

In this note we show that a countable injective module is $\sum $-injective and consequently
a ring $ R $ is left noetherian if the category of left $ R $-modules has a countable injective …

We define below a notion for modules which is dual to that of faithful, and a notion of “fully
divisible” which generalizes that of injectivity. We show that the bicommutator of a cofaithful …

A ring $ R $ is said to have a left Morita duality with a ring $ S $ if there is an additive
contravariant equivalence between two categories of left $ R $-modules and right $ S …

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 …

In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-
crossed modules over a fixed object B, extending the corresponding classical notions to any …