dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Abrams, Gene |
dc.contributor.author |
Aranda Pino, Gonzalo |
dc.contributor.author |
Perera Domènech, Francesc |
dc.contributor.author |
Siles Molina, Mercedes |
dc.date.accessioned |
2007-06-27T14:11:06Z |
dc.date.available |
2007-06-27T14:11:06Z |
dc.date.created |
2007-03 |
dc.date.issued |
2007-03 |
dc.identifier.uri |
http://hdl.handle.net/2072/4245 |
dc.format.extent |
24 |
dc.format.extent |
249699 bytes |
dc.format.mimetype |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;742 |
dc.rights |
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
dc.subject.other |
Àlgebres associatives |
dc.title |
Chain conditions for Leavitt path algebras |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
512 - Àlgebra |
dc.description.abstract |
In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely
many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path
K-algebra L(E) is semisimple. These are precisely the algebras L(E)for which every corner is left (equivalently, right)artinian. They are also precisely the algebras L(E) for which every finitely generated left (equivalently, right) L(E)-module is artinian. In our second main result, we give necessary and sufficient conditions for every corner of L(E) to be left (equivalently, right) noetherian. They also turn out to
be precisely those algebras L(E) for which every finitely generated left(equivalently, right) L(E)-module is noetherian. In both situations, isomorphisms between these algebras and appropriate direct sums of
matrix rings over K or K[x, x−1] are provided. Likewise, in both situations, equivalent graph theoretic conditions on E are presented. |