An additive category A is IBN if and only if there exists an IBN ring R such that A is
equivalent to the full subcategory FR of Mod-R whose objects are all finitely generated free …

Let ${\mathbf {C}} $ be an additive category such that idempotent endomorphisms have
kernels, $ C $ a class of objects of ${\mathbf {C}} $ having Dedekind domains as …

An Azumaya theorem is a deduction of properties of direct sum decompositions of 1 Ci from
conditions on the endomorphism rings of the Ci. The prototype theorems, proved by …

An additive category in which each object has a Krull-Remak-Schmidt decomposition—that
is, a finite direct sum decomposition consisting of objects with local endomorphism rings—is …

This thesis mainly pertains biproduct decompositions of objects in certain additive
categories that exhibit a peculiar regular behaviour. More precisely, in certain additive …

Suppose given an additive category A. It is not necessarily idempotent complete, that is, an
idempotent morphism X e ÝÑ X in A does not necessarily have an image; cf. Definition 45 …

Let R be an associative ring with identity. We determine the minimal nonzero ideals of the
category Mod-R, and find a representation of Mod-R as a subdirect product of subdirectly …

Simple and semisimple additive categories are studied. We prove, for example, that an
artinian additive category is (semi) simple iff it is Morita equivalent to a division ring (oid) …

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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 …