### Abstract

Let D be a division ring and let M_{n}(D) be the ring of all n×n matrices over D with center Z, where n≥2 is an integer. We describe the additive map f: M_{n} (D)→ M_{n} (D) such that f(x)x-xf(x)∈Z for all invertible (singular) x∈M_{n}(D).

Original language | English |
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Pages (from-to) | 318-324 |

Number of pages | 7 |

Journal | Linear Algebra and Its Applications |

Volume | 440 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics