Traces of Permuting n-Derivations and Commutativity of Rings

In this paper, we investigate the commutativity of ring R satisfying certain identities involving the trace delta of permuting n-derivation Delta namely; (i) [delta (x), delta (y)] = [x, y], (ii) delta (x y)+/- x y is an element of Z (R), (iii) delta (x y)+/- y x is an element of Z (R), (iv) delta ([x, y]) = x omicron y, (v) delta (x omicron y) = [x, y], (vi) delta (x) delta (y) = [x, y] for all x, y is an element of R. It is also shown that delta is commuting on a semiprime ring R if it satisfies any one of the identities (i) [delta (x), delta (y)] = 0, (ii) delta ([x, y]) = [delta (x), y], (iii) [delta (x), y] = [x, delta (y)], (iv) delta (x) omicron delta (y) = 0, (v) [delta (x), delta (y)] = y x for all x, y is an element of R.