Characterization of b-generalized Derivations in Rings with Involution

Abstract

AbstractLet \(\mathcal {W}\) be a ring with involution, \(\mathscr {Q}\) be the right Martindale quotient ring, and \(\mathscr {C}\) be the extended centroid of \(\mathcal {W}\). Let \(d: \mathcal {W} \rightarrow \mathscr {Q}\) be an additive map and \(b\in \mathscr {Q}\). An additive map \(\mathfrak {F}:\mathcal {W} \rightarrow \mathscr {Q}\) is called b-generalized derivation with associative map d if \(\mathfrak {F}(xy)=\mathfrak {F}(x)y+bxd(y)\) for all \(x,y\in \mathcal {W}\). In this manuscript, we study commuting b-generalized derivations in rings with involution.KeywordsPrime ringb-generalized derivationInvolution