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    Por favor, use este identificador para citar o enlazar este ítem:https://uvadoc.uva.es/handle/10324/74802

    Título
    A description of ad-nilpotent elements in semiprime rings with involution
    Autor
    Brox López, José Ramón
    García, Esther
    Gómez Lozano, Miguel
    Alcázar, Rubén Muñoz
    Vera de Salas, Guillermo
    Año del Documento
    2021
    Editorial
    Springer Nature
    Descripción
    Producción Científica
    Documento Fuente
    Bulletin of the Malaysian Mathematical Sciences Society, February 2021, vol. 44, n. 4, p.2577-2602.
    Résumé
    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.
    Palabras Clave
    anillos semiprimos, anillos con involución, álgebras de Lie
    ISSN
    0126-6705
    Revisión por pares
    SI
    DOI
    10.1007/s40840-020-01064-w
    Patrocinador
    This work was partially supported by the Centre for Mathematics of the University of Coimbra—UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES. The first author was supported by the Portuguese Government through the FCT Grant SFRH/BPD/118665/2016. The four last authors were partially supported by MTM2017-84194-P (AEI/FEDER, UE), and by the Junta de Andalucía FQM264.
    Version del Editor
    https://link.springer.com/article/10.1007/s40840-020-01064-w
    Idioma
    spa
    URI
    https://uvadoc.uva.es/handle/10324/74802
    Tipo de versión
    info:eu-repo/semantics/publishedVersion
    Derechos
    openAccess
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    • DEP96 - Artículos de revista [95]
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    A description of ad-nilpotent elements in semiprime rings with involution (2021, BMMSS) - Brox, García, Gómez, Muñoz, Vera.pdf
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