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Research Article | Open Access

Supercommuting maps on unital algebras with idempotents

Yingyu Luo1, Yu Wang2( )
College of Mathematics, Changchun Normal University, Changchun 130032, China
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
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Abstract

Let A be a unital algebra with nontrivial idempotents. We considered A as a superalgebra according to Ghahramani and Zadeh's method. We provided a description of supercommuting maps on A. As a consequence, we gave a description of supercommuting maps on matrix algebras, which is different from the result on commuting maps of matrix algebras. Finally, we proved that every supercommuting map on triangular algebras is a commuting map.

Keywords

supercommuting mapcommuting mapgeneralized matrix algebramatrix algebratriangular algebra
CLC number: 15A78, 16W25, 17A70

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 24636-24653
DOI: 10.3934/math.20241200

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Cite this article:
Luo Y, Wang Y. Supercommuting maps on unital algebras with idempotents. AIMS Mathematics, 2024, 9(9): 24636-24653. https://doi.org/10.3934/math.20241200

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Received: 29 June 2024
Revised: 10 August 2024
Accepted: 13 August 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)