Let R be a*-ring with the center Z(R)and N be the set of nonnegative integers.In this paper,it is shown that if R contains a nontrivial self-adjoint idempotent which admits a generalized Lie higher derivable mapping△...Let R be a*-ring with the center Z(R)and N be the set of nonnegative integers.In this paper,it is shown that if R contains a nontrivial self-adjoint idempotent which admits a generalized Lie higher derivable mapping△={G_(n)}_(n∈N)associated with a*-Lie higher derivable mapping L={L_(n)}_(n∈N),then for any X,Y in R and for each n in N there exists an element Z_(X,Y)(depending on X and Y)in the center Z(R)such that G_(n)(X+Y)=G_(n)(X)+G_(n)(Y)+Z_(X,Y).展开更多
基金supported by the MATRICS research grant from DST(SERB)(no.MTR/2017/000033).
文摘Let R be a*-ring with the center Z(R)and N be the set of nonnegative integers.In this paper,it is shown that if R contains a nontrivial self-adjoint idempotent which admits a generalized Lie higher derivable mapping△={G_(n)}_(n∈N)associated with a*-Lie higher derivable mapping L={L_(n)}_(n∈N),then for any X,Y in R and for each n in N there exists an element Z_(X,Y)(depending on X and Y)in the center Z(R)such that G_(n)(X+Y)=G_(n)(X)+G_(n)(Y)+Z_(X,Y).
