Motivated by the study of V-rings, we introduce the concept of V-category, as a Grothendieck category with the property that any simple object is injective. We present basic properties of V-categories, and we study this concept in the special case of locally finitely generated categories, for instance the category R-gr of all graded left R-modules, where R is a graded ring. We use the characterizations of V-categories in the study of graded V-rings. Since V-rings are closely related to Von Neumann regular rings (in the commutative case these classes of rings coincide), the last part of the article is devoted to graded regular rings.
ASJC Scopus subject areas
- Algebra and Number Theory