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Nonlinear (skew-)centralizing mappings on unital algebras with nontrivial idempotents

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Abstract

Let \(\mathcal {R}\) be a commutative ring with unity, and \(\mathcal {A}\) be a unital \(\mathcal {R}\)-algebra with a nontrivial idempotent. Under some mild conditions, we prove that every nonlinear centralizing mapping on \(\mathcal {A}\) is proper. Nonlinear skew-centralizing mapping on \(\mathcal {A}\) is also studied in this paper.

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Authors and Affiliations

  1. School of Mathematics and Big Data, AnHui University of Science & Technology, Huainan, 232001, People’s Republic of China

    Xinfeng Liang & Haonan Guo

Authors
  1. Xinfeng Liang
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  2. Haonan Guo
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Correspondence to Xinfeng Liang.

Additional information

Communicated by Priyanka Grover.

This work was supported by the Youth fund of Anhui Natural Science Foundation (Grant No.2008085QA01) Key projects of University Natural Science Research Project of Anhui Province (Grant No. KJ2019A0107).

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Liang, X., Guo, H. Nonlinear (skew-)centralizing mappings on unital algebras with nontrivial idempotents. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00570-y

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