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Simpleness of Leavitt path algebras with coefficients in a commutative semiring

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Abstract

In this paper, we study ideal- and congruence-simpleness for the Leavitt path algebras of directed graphs with coefficients in a commutative semiring S, establishing some fundamental properties of those algebras. We provide a complete characterization of ideal-simple Leavitt path algebras with coefficients in a commutative semiring S, extending the well-known characterizations when S is a field or a commutative ring. We also present a complete characterization of congruence-simple Leavitt path algebras over row-finite graphs with coefficients in a commutative semiring S.

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Acknowledgments

The authors take an opportunity to express their deep gratitude to the editor for his highly professional handling of our manuscript, as well as to the anonymous referee for an extremely careful reading and working with it and many very valuable suggestions. The second author is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant 101.04–2014.52. The third author has been supported by the Irish Research Council under Research Grant ELEVATEPD/2013/82.

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Authors and Affiliations

  1. Department of Mathematics, Hanover College, Hanover, IN, 47243-0890, USA

    Y. Katsov

  2. Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    T. G. Nam

  3. Institute of Algebra, Dresden University of Technology, Dresden, Germany

    J. Zumbrägel

Authors
  1. Y. Katsov
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  2. T. G. Nam
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  3. J. Zumbrägel
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Correspondence to J. Zumbrägel.

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Communicated by Benjamin Steinberg.

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Katsov, Y., Nam, T.G. & Zumbrägel, J. Simpleness of Leavitt path algebras with coefficients in a commutative semiring. Semigroup Forum 94, 481–499 (2017). https://doi.org/10.1007/s00233-016-9781-1

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  • DOI: https://doi.org/10.1007/s00233-016-9781-1

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