Abstract
Let \({\mathcal {R}}\) be a 2-torsion-free commutative ring with unity, X a locally finite pre-ordered set with a finite number of connected components and \(I(X,{\mathcal {R}})\) the incidence algebra of X over \({\mathcal {R}}\). In this paper, we give a sufficient and necessary condition for a commuting map on \(I(X,{\mathcal {R}})\) to be proper.
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Acknowledgements
The authors would like to thank the referees for their valuable comments and suggestions which significantly helped us improve the final presentation of this paper. 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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Communicated by Hamid Reza Ebrahimi Vishki.
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Jia, H., Xiao, Z. Commuting Maps on Certain Incidence Algebras. Bull. Iran. Math. Soc. 46, 755–765 (2020). https://doi.org/10.1007/s41980-019-00289-1
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DOI: https://doi.org/10.1007/s41980-019-00289-1