Chain conditions for Leavitt path algebras

Gene Abrams; Gonzalo Aranda Pino; Francesc Perera; Mercedes Siles Molina

doi:https://doi.org/10.1515/FORUM.2010.005

Chain conditions for Leavitt path algebras

Gene Abrams, Gonzalo Aranda Pino, Francesc Perera, Mercedes Siles Molina

Research output: Contribution to journal › Article › Research › peer-review

45 Citations (Scopus)

Abstract

In this paper we give necessary and sufficient conditions on a row-finite graph E so that the corresponding (not necessarily unital) Leavitt path K-algebra LK(E) is either artinian or noetherian from both a local and a categorical perspective. These extend the known results in the unital case to a much wider context. Besides the graph theoretic conditions, we provide in both situations isomorphisms between these algebras and appropriate direct sums of matrix rings over K or Kx, x1. © 2010 de Gruyter.

Original language	English
Pages (from-to)	95-114
Journal	Forum Mathematicum
Volume	22
DOIs	https://doi.org/10.1515/FORUM.2010.005
Publication status	Published - 1 Jan 2010

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title = "Chain conditions for Leavitt path algebras",

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AU - Abrams, Gene

AU - Pino, Gonzalo Aranda

AU - Perera, Francesc

AU - Molina, Mercedes Siles

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Y1 - 2010/1/1

N2 - In this paper we give necessary and sufficient conditions on a row-finite graph E so that the corresponding (not necessarily unital) Leavitt path K-algebra LK(E) is either artinian or noetherian from both a local and a categorical perspective. These extend the known results in the unital case to a much wider context. Besides the graph theoretic conditions, we provide in both situations isomorphisms between these algebras and appropriate direct sums of matrix rings over K or Kx, x1. © 2010 de Gruyter.

AB - In this paper we give necessary and sufficient conditions on a row-finite graph E so that the corresponding (not necessarily unital) Leavitt path K-algebra LK(E) is either artinian or noetherian from both a local and a categorical perspective. These extend the known results in the unital case to a much wider context. Besides the graph theoretic conditions, we provide in both situations isomorphisms between these algebras and appropriate direct sums of matrix rings over K or Kx, x1. © 2010 de Gruyter.

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DO - https://doi.org/10.1515/FORUM.2010.005

M3 - Article

SN - 0933-7741

VL - 22

SP - 95

EP - 114

JO - Forum Mathematicum

JF - Forum Mathematicum

ER -

Chain conditions for Leavitt path algebras

Abstract

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