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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...
Let K be a fixed field. We attach to each column-finite quiver E a von Neumann regular K-algebra Q(E) in a functorial way. The algebra Q(E) is a universal localization of the usual path algebra P(E) associated with E. The monoid of isomorphism classes of finitely generated projective right Q(E)-modules is explicitly computed.
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