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A Description of Ad-nilpotent Elements in Semiprime Rings with Involution Brox-López, José Ramón García, Esther Gómez-Lozano, Miguel Ángel Muñoz-Alcázar, Rubén José Vera de Salas, Guillermo Lie, Algebras de In this paper, we study ad-nilpotent elements in Lie algebras arising from semiprime associative rings R free of 2-torsion. With the idea of keeping under control the torsion of R, we introduce a more restrictive notion of ad-nilpotent element, pure ad-nilpotent element, which is a only technical condition since every ad-nilpotent element can be expressed as an orthogonal sum of pure ad-nilpotent elements of decreasing indices. This allows us to be more precise when setting the torsion inside the ring R in order to describe its ad-nilpotent elements. If R is a semiprime ring and a is an element of R is a pure ad-nilpotent element of R of index n with R free of t and ((n)(t))-torsion for t = [n+1/2], then n is odd and there exists lambda is an element of C(R) such that a - lambda is nilpotent of index t. If R is a semiprime ring with involution * and a is a pure ad-nilpotent element of Skew(R,*) free of t and ((n)(t))-torsion for t=[n+1/2], then either a is an ad-nilpotent element of R of the same index n (this may occur if n degrees 1,3(mod4)) or R is a nilpotent element of R of index t+1, and R satisfies a nontrivial GPI (this may occur if n degrees 0,3(mod4)). The case n degrees 2(mod4) is not possible 2024-09-25T17:07:50Z 2024-09-25T17:07:50Z 2024-09-25T17:07:50Z 2021-07 journal article Brox, J., García, E., Lozano, M.G. et al. A Description of Ad-nilpotent Elements in Semiprime Rings with Involution. Bull. Malays. Math. Sci. Soc. 44, 2577–2602 (2021). https://doi.org/10.1007/s40840-020-01064-w https://hdl.handle.net/10630/33314 10.1007/s40840-020-01064-w eng open access Springer Nature