### Abstract

Let R be a semiprime ring with center Z(R). For x; y 2 R, we denote by [x; y] = xy - yx the commutator of x and y. If is a non-identity automorphism of R such that ⋯ [(x^{n0} ); xn1 ]; xn2 ; ⋯ ; xnk = 0 for all x 2 R, where n0; n1; n2; ⋯ ; nk are fixed positive integers, then there exists a map : R ! Z(R) such that (x) = x + (x) for all x 2 R. In particular, when R is a prime ring, R is commutative.

Original language | English |
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Pages (from-to) | 584-592 |

Number of pages | 9 |

Journal | Canadian Mathematical Bulletin |

Volume | 56 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 Sep 1 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Liau, P. K., & Liu, C. K. (2013). On automorphisms and commutativity in semiprime rings.

*Canadian Mathematical Bulletin*,*56*(3), 584-592. https://doi.org/10.4153/CMB-2011-185-5