π-Rickart and dual π-Rickart objects in abelian categories

Abstract

We introduce and study (strongly) [Formula: see text]-Rickart objects and their duals in abelian categories, which generalize (strongly) self-Rickart objects and their duals. We establish general properties of such objects, we analyze their behavior with respect to coproducts, and we study classes all of whose objects are (strongly) [Formula: see text]-Rickart. We derive consequences for module and comodule categories.