Let A and B be modules, which are faithfully flat over their endomorphism ring. The
categories of A-solvable and B-solvable modules coincide if and only if A and B are similar …

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 …

For two bimodules NBA and MAB with M⊗ AN= 0= N⊗ BM, the monomorphism category M
(A, M, N, B) and its dual, the epimorphism E (A, M, N, B), are introduced and studied. By …

The representation theory of a ring Δ has been studied by examining the category of
contravariant (additive) functors from the category of finitely generated left Δ-modules to the …

In the paper [1] Ābrams made a first step in extending the theory of Morita equivalence to
rings without identity. He considered rings in which a set of commuting idempotents is given …

We study Morita equivalence and Morita duality for rings with local units. We extend
Auslander's results on the theory of Morita equivalence and the Azumaya–Morita duality …

In this paper, weak distinguished subcategory and distinguished subcategory of modules
are introduced. Left (right) local unital rings are particularly considered. Also, representable …

In this paper we consider the subcategories CMod-R (M∈ MOD-R st M∼-HomR (R, M)) and
DMod-R (M∈ MOD-R st M⊗ RR∼-R) of the category of all right R-modules, MOD-R, for an …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

In the paper [1] Abrams made a first step in extending the theory of Morita equivalence to
rings without identity. He considered rings in which a set of commuting idempotents is given …