Original Articles

Noetherian quivers

Published in: Quaestiones Mathematicae
Volume 25 , issue 4 , 2002 , pages: 531–538

DOI: 10.2989/16073600209486037

Author(s): Edgar Enochs , J.R. García Rozas , Luis Oyonarte , Sangwon Park

Keywords: QUIVER , NOETHERIAN QUIVER , INJECTIVE COVER , REPRESENTATIONS OF QUIVERS

Abstract

Noetherian quivers have been studied and characterized (when the number of arrows is finite) by Höinghaus 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.

« Universal harmonic functions

Convergence of ray sequences of Padé approximants for ₂ f ₁(a, 1; c; z), (c > a > 0) »