### 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 L K(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 L K(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 L K(E). © 2014 Elsevier Inc.

Original language | English |
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Pages (from-to) | 333-352 |

Journal | Journal of Algebra |

Volume | 417 |

DOIs | |

Publication status | Published - 1 Nov 2014 |

### Keywords

- Finitely presented module
- Leavitt path algebra
- Primitive ideal
- Simple module

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## Cite this

Ara, P., & Rangaswamy, K. M. (2014). Finitely presented simple modules over Leavitt path algebras.

*Journal of Algebra*,*417*, 333-352. https://doi.org/10.1016/j.jalgebra.2014.06.032