TWO-SIDED CHAIN CONDITIONS IN LEAVITT PATH ALGEBRAS OVER ARBITRARY GRAPHS-Reference-Cited by-同舟云学术

TWO-SIDED CHAIN CONDITIONS IN LEAVITT PATH ALGEBRAS OVER ARBITRARY GRAPHS

Published:2012-05-24 Issue:03 Volume:11 Page:1250044
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

ABRAMS GENE¹,BELL JASON P.²,COLAK PINAR²,RANGASWAMY KULUMANI M.¹

Affiliation:

1. University of Colorado, Colorado Springs, CO 80918, USA

2. Simon Fraser University, Burnaby, BC V5A1S6, Canada

Abstract

Let E be any directed graph, and K be any field. For any ideal I of the Leavitt path algebra LK(E) we provide an explicit description of a set of generators for I. This description allows us to classify the two-sided noetherian Leavitt path algebras over arbitrary graphs. This extends similar results previously known only in the row-finite case. We provide a number of additional consequences of this description, including an identification of those Leavitt path algebras for which all two-sided ideals are graded. Finally, we classify the two-sided artinian Leavitt path algebras over arbitrary graphs.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498811005713

Reference13 articles.

1. The Leavitt path algebra of a graph

2. Locally finite Leavitt path algebras

3. The socle series of a Leavitt path algebra

4. The socle of a Leavitt path algebra

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