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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)
##### Keywords:
differential identities; prime rings; right ideals; derivations