Per citar aquest document: http://ddd.uab.cat/record/44044
Chain conditions for Leavitt path algebras
Abrams, Gene
Aranda Pino, Gonzalo
Perera Domènech, Francesc
Siles Molina, Mercedes
Centre de Recerca Matemàtica

Publicació: Centre de Recerca Matemàtica 2007
Descripció: 24 p.
Col·lecció: Prepublicacions del Centre de Recerca Matemàtica ; 742
Resum: 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.
Drets: 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 Creative Commons
Llengua: Anglès.
Document: preprint
Matèria: Àlgebres associatives

Adreça alternativa: http://hdl.handle.net/2072/4245


24 p, 243.8 KB

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