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Linear \(n\)-commuting maps on incidence algebras

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Abstract

Let \(n\) be a positive integer and \(\mathcal{R}\) be a \(2\) and \(n!\)-torsion free commutative ring with unity. Let \(X\) be a locally finite pre-ordered set. If any two directed edges in each connected component of the complete Hasse diagram \((X,\mathfrak{D})\) are contained in one cycle, then every \(n\)-commuting map on the incidence algebra \(I(X,\mathcal{R})\) is proper.

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Acknowledgement

The authors thank the referee for valuable comments and suggestions.

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Authors and Affiliations

  1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, 362021, P. R. China

    Z.-K. Xiao

  2. School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, 362021, P. R. China

    L.-Q. Yang

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  1. Z.-K. Xiao
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  2. L.-Q. Yang
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Corresponding author

Correspondence to Z.-K. Xiao.

Additional information

This work is supported in part by the NSF of Fujian Province (No. 2018J01002), Program for Innovative Research Team in Science and Technology in Fujian Province University, and Quanzhou High-Level Talents Support Plan (No. 2017ZT012).

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Xiao, ZK., Yang, LQ. Linear \(n\)-commuting maps on incidence algebras. Acta Math. Hungar. 164, 470–483 (2021). https://doi.org/10.1007/s10474-021-01148-4

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  • DOI: https://doi.org/10.1007/s10474-021-01148-4

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