Chain conditions for Leavitt path algebras
By G. Abrams, G. Pino, F. Perera, Mercedes Siles Molina. 2009
73 citations recorded by the source corpus.
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 K[x, x –1].
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5abff0afff4ed1255027edbdb5afe5cbedb0f758
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In Algebra and Number Theory
- Mercedes Siles Molina
- Cándido Martín González
- D. M. Barquero
- G. Pino
- G. Abrams
- M. Tomforde
- Xiao-Wu Chen
- Kulumani M. Rangaswamy
In Geometry and Topology
- G. Pino
- Cándido Martín González
- D. M. Barquero
- Mercedes Siles Molina
- Xiao-Wu Chen
- G. Abrams
- M. Tomforde
- K. Goodearl
In Mathematical Physics
- Mercedes Siles Molina
- Cándido Martín González
- D. M. Barquero
- G. Pino
- G. Abrams
- M. Tomforde
- Xiao-Wu Chen
- Kulumani M. Rangaswamy
Citations in the corpus
- Socle theory for Leavitt path algebras of arbitrary graphs (2008, methodology): “In addition, several other ring properties were studied in the case of row-finite L eavitt path algebras, such as being exchange [10], finite dimensional [5], noetherian [6] , semisimple [ 4 ] or having stable rank [10, 8]. It has been also shown that the Leavitt path algebra LK(E) of a graph E and ”