By using the correspondence between locally finitely presented additive categories and
rings with enough idempotents, we study several properties of such rings in terms of the …

Let Mod-S denote the category of S-modules, where S is a small pre-additive category.
Using the notion of relative derived categories of functor categories, we generalize Rickard's …

Let A and B be associative rings with unit, Mod-A and Mod-B categories of unital right A-
modules and unital right B-modules respectively. For an AB-bimodule* UB, we consider two …

Rg be a G-graded ring. It is well known (see eg [D],[M1],[N],[NRV],[NV]) that in the study of
the connections that may be established between the categories R-gr of graded R-modules …

In this article, FP-injective complexes are introduced and studied. We prove that (⊥ ℱℐ, ℱℐ)
is a hereditary cotorsion theory if and only if R is a left coherent ring, where ℱℐ denotes the …

Let k be a field. We show that locally presentable, k-linear categories CC dualizable in the
sense that the identity functor can be recovered as ∐ _i x_i ⊗ f_i∐ ixi⊗ fi for objects x_i ∈ C …

Let 𝒜 and ℬ be two Grothendieck categories, R: 𝒜→ ℬ, L: ℬ→ 𝒜 a pair of adjoint functors,
S∈ ℬ a generator, and U= L (S). U defines a hereditary torsion class in 𝒜, which is carried …

For a nonempty topological space $ X $, the ring of all real-valued functions on $ X $ with
pointwise addition and multiplication is denoted by $ F (X) $ and contonuous members of …

In this article, we present $ GPW $-flatness property of acts over monoids, which is a
generalization of principal weak flatness. We say that a right $ S $-act $ A_ {S} $ is $ GPW …

For a category, we investigate the problem of when the coproduct⊕ and the product
functor∏ from I to are isomorphic for a fixed set I, or, equivalently, when the two functors …