### Abstract

Let R be a noncommutative prime ring with the extended centroid C, I a nonzero ideal of R and g a b-generalized derivation of R. We show that, if [g(x^{m}), x^{n}]=0 for all x ϵ I, where m, n, k are fixed positive integers, then there exists ϵ λ C such that g(x) for all xϵR unless R ≅ M_{2}(GF(2)), the 2x2 matrix ring over the Galois field GF(2) of two elements. This gives a natural generalization of the results for derivations, generalized derivations and generalized σ -derivations with an X-inner automorphism σ.

Original language | English |
---|---|

Pages (from-to) | 300-312 |

Number of pages | 13 |

Journal | Linear and Multilinear Algebra |

Volume | 65 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2017 Feb 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory