On skew derivations of semiprime rings (Q1190742)

The author proves the following two fundamental results: i) Let a semiprime ring \(R\) satisfy a multilinear identity with automorphisms and skew derivations \(f(x_ 1,\dots,x_ n) = 0\), where \(f(x_ i)\) is a reduced polynomial. Then Martindale's left quotient ring \(R_{\mathcal F} = \underset{\to}{\lim\text{Hom}}({_ RI,R})\) satisfies a GPI; ii) If a semiprime ring \(R\) with 1 satisfies a multilinear essential identity with automorphisms and skew derivations and every automorphism commutes with an arbitrary skew derivation then \(R\) is a PI-ring.