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

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 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 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 give a constructive sufficient condition for a matrix over a commutative ring to be von
Neumann regular, and we show that it is also necessary over local rings. Specifically, we …

We study the transfer via functors between abelian categories of the (dual) relative splitness
of objects with respect to a fully invariant short exact sequence. We mainly consider fully …

In this paper,(dual) purely Rickart objects are introduced as generalizations of (dual) Rickart
objects in Grothendieck categories. Examples showing the relations between (dual) relative …

We investigate relative CS-Baer objects in abelian categories in relationship with other
relevant classes of objects such as relative Baer objects, extending objects, objects having …