NISC South Africa

Quaestiones Mathematicae 2002, 25 (4) : 531–538
© NISC (pty) Ltd. www.nisc.co.za

Noetherian quivers

<< Previous Abstract :: Next Abstract >>

Authors: E Enochs¹ , JR García Rozas² , L Oyonarte² and S Park³

¹Department of Mathematics, Dong-A University, Pusan, Korea
²Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA
³Dept. de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain

Corresponding Author: E Enochs (E-mail: enochs@mis.uky.edu)

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

Keywords: Quiver; noetherian quiver; injective cover; representations of quivers

Link to fulltext on Ingenta: Full Text on Ingenta