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Leavitt path algebras are Bézout

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Abstract

Let E be a directed graph, K any field, and let LK(E) denote the Leavitt path algebra of E with coefficients in K. We show that LK(E) is a Bézout ring, i.e., that every finitely generated one-sided ideal of LK(E) is principal.

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Author information

Authors and Affiliations

  1. University of Colorado, Colorado Springs, CO, 80918, USA

    Gene Abrams

  2. Università degli Studi di Verona, I-37134, Verona, Italy

    Francesca Mantese

  3. Università degli Studi di Padova, I-35121, Padova, Italy

    Alberto Tonolo

Authors
  1. Gene Abrams
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  2. Francesca Mantese
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  3. Alberto Tonolo
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Corresponding author

Correspondence to Gene Abrams.

Additional information

Dedicated to the memory of Frank W. Anderson: teacher, scholar, friend.

The first author was partially supported by a Simons Foundation Collaboration Grants for Mathematicians Award #208941. The second and third authors were supported by Progetto di Eccellenza Fondazione Cariparo “Algebraic structures and their applications: Abelian and derived categories, algebraic entropy and representation of algebras”.

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Abrams, G., Mantese, F. & Tonolo, A. Leavitt path algebras are Bézout. Isr. J. Math. 228, 53–78 (2018). https://doi.org/10.1007/s11856-018-1773-2

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  • DOI: https://doi.org/10.1007/s11856-018-1773-2

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