Supercommuting maps on unital algebras with idempotents

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.