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) 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) 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).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
