To any additive category, we associate in a functorial way two additive categories A (), B ().
The category A (), resp. B (), is the reflection of in the category of additive categories with …

We study the transfer of (dual) relative Rickart properties via functors between abelian
categories, and we deduce the transfer of (dual) relative Baer property. We also give …

We study the transfer of Baer-Kaplansky classes via additive functors between preadditive
categories. We show that the Baer-Kaplansky property is well behaved with respect to fully …

Let R be an associative ring with identity. A right R-module M is called cotorsion if Ext"(F,
M)= 0 for every flat right R-module F. These modules were introduced by Harrison [21] in the …

JL GARCIA(MURCIA) AND D. SIMSON(TORU N) 1. Introduction. Throughout this paper, by
a ring we shall mean “a ring with enough idempotents” in the sense of [4] and [26, p. 464] …

The classical Cantor-Bernstein-Schröder Theorem states that if A and B are two sets such
that there exist injective functions f: A→ B and g: B→ A, then there exists a bijection between …

The notion of FTF ring (see Definition 1.1 or Proposition 1.2) captures homological and
finiteness properties shared by several classes of rings. Thus coherent rings with left ffat …

Let ℰ be an additive category and 𝒞 a full subcategory with split idempotents, and closed
under isomorphic images and finite direct sums. We give conditions on ℰ and 𝒞 implying …