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    Imagens de polinômios multilineares sobre algumas subálgebras de matrizes
    (Universidade Federal de São Paulo (UNIFESP), 2019-01-18) Fagundes, Pedro Souza [UNIFESP]; Mello, Thiago Castilho De [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
    In this dissertation we will study the images of multilinear polynomials on matrix algebras. We will present results from Shoda, Albert and Muckenhoupt, Mesyan and Buzinski and Winstanley to study the cases where the multilinear polynomials have degree up to four. We will also describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra as well as the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra. Moreover, we will study some results from Brešar and Klep about the relation between the linear span of the images of noncommutative polynomials on algebras and Lie ideals.