### Abstract

Let R be a prime ring with a nonzero derivation d and let f (X _{1},...,X_{t}) be a multilinear polynomial over C, the extended centroid of R. Suppose that b[d(f(x_{1},...,x_{t})), f(x1,...,x_{t})]_{n} = 0 for all x_{i} ∈ R, where 0 ≠ b ∈ R and n is a fixed positive integer. Then f(X_{1},..., X_{t}) is centrally valued on R unless char R = 2 and dim_{C} RC = 4. We prove a more generalized version by replacing R with a left ideal.

Original language | English |
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Pages (from-to) | 719-725 |

Number of pages | 7 |

Journal | Communications in Algebra |

Volume | 33 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Dec 5 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory