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 introduce and study (dual) strongly relative Rickart objects in abelian categories. We
prove general properties, we analyze the behaviour with respect to (co) products, and we …

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 …

We study the transfer of (dual) relative CS-Rickart properties via functors between abelian
categories. We consider fully faithful functors as well as adjoint pairs of functors. We give …

We introduce and study relative Rickart objects and dual relative Rickart objects in abelian
categories. We show how our theory may be employed in order to study relative regular …

We introduce relative CS-Rickart objects in abelian categories, as common generalizations
of relative Rickart objects and extending objects. We study direct summands and (co) …

We introduce and investigate weak relative Rickart objects and dual weak relative Rickart
objects in abelian categories. Several types of abelian categories are characterized in terms …

In an arbitrary Grothendieck category, we find necessary and sufficient conditions for the
class of FP n-injective objects to be a torsion class. By doing so, we propose a notion of n …

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 𝒜 and ℬ be two Grothendieck categories, R: 𝒜→ ℬ, L: ℬ→ 𝒜 a pair of adjoint functors,
S∈ ℬ a generator, and U= L (S). U defines a hereditary torsion class in 𝒜, which is carried …