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

2018/12/19 by Bennis, Driss, Dhara, Basudeb, Fahid, Brahim
#16N60 #16W25 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1812.08209

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. Fošner, On Generalized (m, n)-Derivations and Generalized (m, n)-Jordan Derivations in Rings, Algebra Colloq. 21 (2014), 411--420] and [A. Fošner, A note on generalized (m,n)-Jordan centralizers, Demonstratio Math. 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).

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