On Generalized $(m, n)$-Jordan Derivations and Centralizers of Semiprime Rings

Driss Bennis; Basudeb Dhara; Brahim Fahid

On Generalized $(m, n)$-Jordan Derivations and Centralizers of Semiprime Rings

Rings and Algebras 2018-12-21 v1

Authors: Driss Bennis , Basudeb Dhara , Brahim Fahid

Abstract

In this paper we give an affirmative answer to two conjectures on generalized $(m,n)$ -Jordan derivations and generalized $(m,n)$ -Jordan centralizers raised in [S. Ali and A. Fo\v{s}ner, \textit{On Generalized $(m, n)$ -Derivations and Generalized $(m, n)$ -Jordan Derivations in Rings,} Algebra Colloq. \textbf{21} (2014), 411--420] and [A. Fo\v{s}ner, \textit{A note on generalized $(m,n)$ -Jordan centralizers,} Demonstratio Math. \textbf{46} (2013), 254--262]. Precisely, when $R$ is a semiprime ring, we prove, under some suitable torsion restrictions, that every nonzero generalized $(m,n)$ -Jordan derivation (resp., a generalized $(m,n)$ -Jordan centralizer) is a derivation (resp., a two-sided centralizer).

Keywords

semiprime rings generalized jordan derivations generalized jordan centralizers torsion restrictions ring theory

Cite

@article{arxiv.1812.08209,
  title  = {On Generalized $(m, n)$-Jordan Derivations and Centralizers of Semiprime Rings},
  author = {Driss Bennis and Basudeb Dhara and Brahim Fahid},
  journal= {arXiv preprint arXiv:1812.08209},
  year   = {2018}
}

Comments

This paper is a part of Fahid's PhD thesis which is defended on 17 march 2018

On Generalized $(m, n)$-Jordan Derivations and Centralizers of Semiprime Rings

Abstract

Keywords

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