This analysis describes images of generalized multilinear polynomials in upper triangular matrix algebras, suggesting a broad application of the Fagundes–Mello conjecture's results.
A polynomial is called a generalized multilinear polynomial if it is a sum of some multilinear polynomials over a field. The goal of this paper is to give a description of the images of generalized multilinear polynomials on upper triangular matrix algebras, generalizing all results of the Fagundes–Mello conjecture proposed by Fagundes and Mello in 2019.
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Chen et al. (2025) studied this question.
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