Abstract
The objective of this research is to prove that an additive mapping T : R. R is a left as well as right centralizer on R if it satisfies any one of the following identities: (i) T(x(n)y(n) + y(n)x(n)) = T(x(n))y(n) + y(n)T(x(n)) (ii) 2T(x(n)y(n)) = T(x(n))y(n) + y(n)T(x(n)) for each x, y epsilon R, where n >= 1 is a fixed integer and R is any n!-torsion free semiprime ring. In addition, we talk over above identities in the setting of *-ring(ring with involution).