A note on the regular ideals of Leavitt path algebras

@article{Gonccalves2021ANO,
  title={A note on the regular ideals of Leavitt path algebras},
  author={Daniel Gonccalves and Danilo Royer},
  journal={Journal of Algebra and Its Applications},
  year={2021}
}
We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As a consequence, for a row-finite graph, we obtain that the quotient of the associated Leavitt path by a regular ideal is again a Leavitt path algebra and that Condition (L) is preserved by quotients by regular ideals. Furthermore, we describe the vertex set of a regular ideal and make a comparison between the theory of regular ideals in Leavitt path algebras and in graph C*-algebras. 
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