TY - JOUR
T1 - V-categories
T2 - Applications to graded rings
AU - Dǎuş, L.
AU - Nǎstǎsescu, C.
AU - van Oystaeyen, F.
PY - 2009/9
Y1 - 2009/9
N2 - 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.
AB - 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.
KW - V-categories
UR - http://www.scopus.com/inward/record.url?scp=70449569297&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70449569297&partnerID=8YFLogxK
U2 - 10.1080/00927870802502720
DO - 10.1080/00927870802502720
M3 - Article
AN - SCOPUS:70449569297
SN - 0092-7872
VL - 37
SP - 3248
EP - 3258
JO - Communications in Algebra
JF - Communications in Algebra
IS - 9
ER -