Abstract
Let R be a prime ring with involution * and d be a nonzero derivation on R such that d(x *) = -d(x)* for all x ∈ R. Suppose that n ≥ 1 is a fixed integer. Then (I) if d(s) n = 0 for all s = s *, then R is either a commutative domain or an order in a 4-dimensional central simple algebra; (II) if d(s) n ∈Z, the center of R for all s = s *, then R is either a commutative domain or an order in a simple algebra of dimension 4 or 16 over its center.
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