Maximal nilpotent subalgebras I: Nilradicals and Cartan subalgebras in associative algebras. With 428 exercises

Focusing on the exploration of Cartan subalgebras in Lie algebras related to associative algebras, the author expands on Salvatore Siciliano's theories during their doctoral studies. The work delves into maximal nilpotent substructures, particularly the nilradical, and emphasizes the relationship between these substructures and the associative properties of the underlying algebras. Numerous examples, such as group algebras and Solomon algebras, are provided to illustrate the concepts, along with exercises that encourage readers to engage with the theory more deeply.