We prove the following Baer-Kaplansky Theorem in additive categories. If M and N are
objects of an additive category C such that:(1) M= A⨁ X and N= B⨁ X for some objects A, B …

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Abstract We study Baer–Kaplansky classes in Grothendieck categories. We apply our results
to functor categories, and discuss the transfer of the Baer–Kaplansky property to finitely …

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 …

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 …

In this paper, we obtain a non-abelian analogue of Lubkin's embedding theorem for abelian
categories. Our theorem faithfully embeds any small regular Mal'tsev category C in an n-th …

It is well known that the Baer criterion for injectivity of R-modules, for a ring R with unit, is not
true in a general category, even in a general abelian category. In this paper, we prove some …

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 …

Given any additive category C with split idempotents, pseudokernels and pseudocokernels,
we show that a subcategory B is coreflective if, and only if, it is precovering, closed under …

In this paper we give necessary and sufficient conditions for an additive functor u: u→ C,
from a small pre-additive category u to a Grothendieck category C, to realize C as a …