Article ID Journal Published Year Pages File Type
4584664 Journal of Algebra 2014 20 Pages PDF
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).

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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