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Derivations on one-sided ideals of prime rings. (English) Zbl 1002.16028
Using the theory of differential identities the authors prove the following result: Let \(R\) be a prime ring, \(T\) a nonzero right ideal of \(R\), \(D\) a nonzero derivation of \(R\), and \(n\) a fixed positive integer. If \(D(x)x^n=0\) for \(x\in T\) then \(D(T)T=0\), and if \(x^nD(x)=0\) for all \(x\in T\) then \(R\cong M_2(\text{GF}(2))\).

MSC:
16W25 Derivations, actions of Lie algebras
16N60 Prime and semiprime associative rings
16R50 Other kinds of identities (generalized polynomial, rational, involution)
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