TRACES OF PERMUTING n-ADDITIVE MAPPINGS IN ∗-PRIME RINGS

In this paper, we prove that a nonzero square closed ∗-lie ideal u of a ∗-prime ring r of char r ≠ (2^n − 2) is central,if one of the following holds: (i)δ(x)δ(y)∓x◦ y ∈ z(r), (ii)[x, y]−δ(xy)δ(yx) ∈ z(r), (iii)δ(x)◦δ(y)∓[x, y] ∈ z(r), (iv)δ(x)◦δ(y)∓xy ∈ z(r), (v)δ(x)δ(y) ∓ yx ∈ z(r), where δ is the trace of n-additive map f : r × r × .... × r n−times−→ r, for all x, y ∈ u.