Main Article Content
Noetherian Quivers
Abstract
Noetherian quivers have been studied and
characterized (when the number of arrows is finite) by Höinghuas and Richter in
[10]. In this paper we give a characterization of noetherian quivers in the
most general case in Theorem 3.6. We prove that a quiver is noetherian if and
only if the rooted tree associated to any vertex satisfies some sort of
finiteness condition, if and only if every finitely generated representation
over a noetherian ring has an injective cover.
Mathematics Subject
Classification (2000): Primary 16G20; Secondary 18A25
Quaestiones Mathematicae 25 (2002), 531-538
characterized (when the number of arrows is finite) by Höinghuas and Richter in
[10]. In this paper we give a characterization of noetherian quivers in the
most general case in Theorem 3.6. We prove that a quiver is noetherian if and
only if the rooted tree associated to any vertex satisfies some sort of
finiteness condition, if and only if every finitely generated representation
over a noetherian ring has an injective cover.
Mathematics Subject
Classification (2000): Primary 16G20; Secondary 18A25
Quaestiones Mathematicae 25 (2002), 531-538
