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 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 investigate (dual) relative split objects with respect to a fully invariant short
exact sequence in abelian categories. We compare them with (dual) relative Rickart objects …

We introduce (dual) strongly relative CS-Rickart objects in abelian categories, as common
generalizations of (dual) strongly relative Rickart objects and strongly extending (lifting) …

For a G-graded ring R, the problem of Gr-regularity (ie von Neumann regularity condition on
homogeneous elements) has been treated earlier (see Năstăsescu and Van Oystaeyen …

We introduce for any Grothendieck category the notion of stable localizing subcategory, as a
localizing subcategory that can be written as an intersection of localizing subcategories …