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A description of ad-nilpotent elements in semiprime rings with involution Brox López, José Ramón García, Esther Gómez Lozano, Miguel Alcázar, Rubén Muñoz Vera de Salas, Guillermo Producción Científica 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 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 L in the extended centroid such that a-L 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=1,3 mod 4) or R is a nilpotent element of R of index t+1, and R satisfies a nontrivial GPI (this may occur if n=0,3 mod 4). The case is n=2 mod 4 not possible. 2025-02-03T05:20:14Z 2025-02-03T05:20:14Z 2021 info:eu-repo/semantics/article Bulletin of the Malaysian Mathematical Sciences Society, February 2021, vol. 44, n. 4, p.2577-2602. 0126-6705 https://uvadoc.uva.es/handle/10324/74802 10.1007/s40840-020-01064-w 2577 4 2602 Bulletin of the Malaysian Mathematical Sciences Society 44 2180-4206 spa https://link.springer.com/article/10.1007/s40840-020-01064-w info:eu-repo/semantics/openAccess Springer Nature SI