Abstract
Let R be a non-commutative prime ring of characteristic different from 2, Qr its right Martindale quotient ring and C its extended centroid. Suppose that L is a non-central Lie ideal of R, F a non-zero generalized skew derivation of R and a fixed integer. If for all then one of the following holds: R satisfies the standard polynomial identity on four non-commuting variables; there exists such that for all with
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