Let be an associative prime ring of with center and extended centroid , a nonzero multilinear polynomial over in noncommuting variables, a nonzero derivation of and a nonzero right ideal of . We prove that: (i) if for all , then for some idempotent element in the socle of and is central-valued in unless is an inner derivation induced by such that and ; (ii) if for all , then for some idempotent element in the socle of and either is central in or satisfies the standard identity unless is an inner derivation induced by such that and .
Basudeb Dhara, Rajendra K. Sharma, Right Sided Ideals and Multilinear Polynomials with Derivation on Prime Rings. Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 243–257
DOI 10.4171/RSMUP/121-15