Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584664 | Journal of Algebra | 2014 | 20 Pages |
Abstract
Let E be an arbitrary graph and K be any field. We construct various classes of non-isomorphic simple modules over the Leavitt path algebra LK(E)LK(E) induced by vertices which are infinite emitters, closed paths which are exclusive cycles and paths which are infinite, and call these simple modules Chen modules. It is shown that every primitive ideal of LK(E)LK(E) can be realized as the annihilator ideal of some Chen module. Our main result establishes the equivalence between a graph theoretic condition and various conditions concerning the structure of simple modules over LK(E)LK(E).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pere Ara, Kulumani M. Rangaswamy,