Noetherian quivers

Authors: Enochs, Edgar; Rozas, J.R. García; Oyonarte, Luis; Park, Sangwon

Source: Quaestiones Mathematicae, Volume 25, Number 4, 1 December 2002 , pp. 531-538(8)

Publisher: NISC Pty Ltd

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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.

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

Document Type: Research article

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