RT Journal Article
T1 A Description of Ad-nilpotent Elements in Semiprime Rings with Involution
A1 Brox-López, José Ramón
A1 García, Esther
A1 Gómez-Lozano, Miguel Ángel
A1 Muñoz-Alcázar, Rubén José
A1 Vera de Salas, Guillermo
K1 Lie, Algebras de
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 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
PB Springer Nature
YR 2021
FD 2021-07
LK https://hdl.handle.net/10630/33314
UL https://hdl.handle.net/10630/33314
LA eng
NO 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
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026