RT info:eu-repo/semantics/article
T1 A description of ad-nilpotent elements in semiprime rings with involution
A1 Brox, Jose
A1 García, Esther
A1 Lozano, Miguel Gómez
A1 Alcázar, Rubén Muñoz
A1 de Salas, Guillermo Vera
K1 anillos semiprimos, anillos con involución, álgebras de Lie
AB 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.
PB Springer Nature
SN 0126-6705
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/74802
UL https://uvadoc.uva.es/handle/10324/74802
LA spa
NO Bulletin of the Malaysian Mathematical Sciences Society, February 2021, vol. 44, n. 4, p.2577-2602.
NO Producción Científica
DS UVaDOC
RD 05-feb-2025