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Purely Infinite Simple Ultragraph Leavitt Path Algebras

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Abstract

In this article, we give necessary and sufficient conditions under which the Leavitt path algebra \(L_K(\mathcal {G})\) of an ultragraph \(\mathcal {G}\) over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over \(K[x, x^{-1}]\), or a purely infinite simple algebra.

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Acknowledgements

The first author was partially supported by the Vietnam Academy of Science and Technology Grant CT0000.02/20-21. The authors take an opportunity to express their deep gratitude to the anonymous referee for extremely careful reading, highly professional working with our manuscript, and valuable suggestions.

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Correspondence to N. D. Nam.

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Nam, T.G., Nam, N.D. Purely Infinite Simple Ultragraph Leavitt Path Algebras. Mediterr. J. Math. 19, 7 (2022). https://doi.org/10.1007/s00009-021-01899-y

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  • DOI: https://doi.org/10.1007/s00009-021-01899-y

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