There are no nontrivial two-sided multiplicative (generalized)-skew derivations in prime rings

  1. José Brox 1
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

Revista:
ArXiv.org

ISSN: 2331-8422

Año de publicación: 2020

Tipo: Artículo

DOI: 10.48550/ARXIV.2007.08013 GOOGLE SCHOLAR

Otras publicaciones en: ArXiv.org

Resumen

As originally defined by Ashraf and Mozumder, multiplicative (generalized)-skew derivations must satisfy two identities. In this short note we show that, as a consequence of the simultaneous satisfaction of both identities, a multiplicative (generalized)-skew derivation of a prime ring is either a multiplicative (generalized) derivation (i.e., not skew), or a generalized skew derivation (i.e., additive). Therefore only one of the identities should be taken in the definition of multiplicative (generalized)-skew derivations in order to get a new class of derivations in prime rings.