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math.RA2025
Commutators on Generalized Block-Triangular Algebras
Pedro Souza Fagundes, Thiago Castilho de Mello
The characterization of commutators in associative algebras is a classical problem in ring theory. In this paper, we address this problem for the natural class of generalized block…
math.RA2025
On the PI-exponent of matrix algebras and algebras with generalized actions
Thiago Castilho de Mello, Felipe Yukihide Yasumura
We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let be a PI-algebra with a positi…
math.RA2025
Identities of relatively free algebras of Lie nilpotent associative algebras
Elitza Hristova, Thiago Castilho de Mello
In this paper, we consider the relatively free algebra of rank , , in the variety of Lie nilpotent associative algebras of index , denoted by $\mathfrak{…