We generalize the Morita theorems to certain functor categories using properties of adjoint
functors. Let sé and 38 be categories. Recall that sé and 38 are said to be equivalent if there …

Let C be an abelian category. Then for any object C in C,~ xt'(C,) is defined as a covariant
functor from C to Ab such that for each X in C EX~'(C, X) is an additive group consisting of …

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 …

0.1. In this paper we introduce the notion of the basic ring of a] ocally artinian Grothendieck
category cg. Namely let W be the minimal injective cogenerator of~ g, 9] the subcategory of …

It is an old observation of Eckmann-Hilton [21], that the homotopy theory of topological
spaces has an algebraic analogue in the module category of a ring. Inspired by the work of …

Let R be a ring with identity. RM Thrall defined a QF-3 algebra in [3] and many authors
defined QF-3 rings and studied them (cf.[10]). R is called right QF-3 if R has a minimal a …

This is mainly a summary and commentary of the article [3] with the same title. Proofs are
generally omitted here, and so is the treatment of relative K-theory. On the other hand …

The unit element of a ring A plays an important part in classical module theory. Its existence
is equivalent to the adjointness of the free functor from the base category of abelian groups …

The starting point for the ideas in this paper is a result of Kevin Burke [2, Prop 3.2. 5] in the
model theory of modules. This result establishes a correspondence between syntactically …

The aim of this paper is to study a property of a special kind of exact functors and give some
applications to projective modules and injective modules. In section 1 we introduce the …