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arXiv · 1507.02913

Simpleness of Leavitt Path Algebras with Coefficients in a Commutative Semiring

Yefim Katsov·Tran Giang Nam·Jens Zumbrägel
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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, as well as establish some fundamental properties of those algebras. We provide a complete characterization of ideal-simple Leavitt path algebras with coefficients in a semifield S that extends the well-known characterizations when the ground semiring S is a field. Also, extending the well-known characterizations when S is a field or commutative ring, we 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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Yefim Katsov, Tran Giang Nam, Jens Zumbrägel. 2015-07-10. Simpleness of Leavitt Path Algebras with Coefficients in a Commutative Semiring. https://doi.org/10.1007/s00233-016-9781-1

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