In various questions in ring theory the followin tegory turns out to be useful (cf.[3-S]). For an
arbitrary ring R let mod R be the category of finitely presented right R-modules (viewed as a …

The considerable number of papers by various authors dealing with Morita duality of module
categories, makes it obvious that the theory of Morita duality can be treated purely on a …

Weak relative Rickart objects generalize relative Rickart objects in abelian categories. We
study how such a property is preserved or reflected by fully faithful functors and adjoint pairs …

The purpose of this paper is twofold: on the one hand we give criteria, in a categorical
context, for a shape-invariant functor to be a Kan extension; on the other hand we apply our …

The notions of Category and Punotor lead naturally to the following question. Given a ring A,
can one char acterize those rings B with the property that there ex*-ists a covariant functor …

For any additive functor from a category of modules into an abelian category there is a
largest Giraud subcategory for which the functor acts faithfully on homomorphisms into the …

([N~], Corollaire 1.3). In fact f is equivalent to the category of right modules over a right
artinian ring ([N~], ThEorSme 3.3) and thus the Hopkins-Levitzki theorem in a Grothendieck …

Let A be a Grothendieck category with an artinian generator, that is a generator satisfying
the descending chain condition on subobjects. C. NLstL-sescu [lo] proved that A is …

Theorem 1. Let be a small abelian category. Then there is a full, faithful, exact functor Mod-
R, the category of right R-modules. It has long seemed to me that this theorem should be the …

We show how the theory of (dual) strongly relative Rickart objects may be employed in order
to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian …