X-generalized skew derivations behaving as weak Jordan right η-centralizers in prime rings

Abstract

Consider a prime ring R which is noncommutative with the maximal left ring of quotients of R denoted by Q m l ( R ) and the extended centroid C . An additive map G : R → Q m l ( R ) satisfying G ( g 2 ) + η g G ( g ) ∈ C for all g ∈ R , where η ∈ C is called a weak Jordan right η-centralizer. In this paper, we establish the characterization of weak Jordan right η-centralizers in prime rings. As an application, we describe X-generalized skew derivations which behave like weak Jordan right η-centralizers.