Let $ \mathcal{A} $ be a unital algebra with nontrivial idempotents. We considered $ \mathcal{A} $ as a superalgebra according to Ghahramani and Zadeh's method. We provided a description of supercommuting maps on $ \mathcal{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.
Citation: Yingyu Luo, Yu Wang. Supercommuting maps on unital algebras with idempotents[J]. AIMS Mathematics, 2024, 9(9): 24636-24653. doi: 10.3934/math.20241200
Let $ \mathcal{A} $ be a unital algebra with nontrivial idempotents. We considered $ \mathcal{A} $ as a superalgebra according to Ghahramani and Zadeh's method. We provided a description of supercommuting maps on $ \mathcal{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.
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