Centralizing maps on invertible or singular matrices over division rings

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Let D be a division ring and let Mn(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: Mn (D)→ Mn (D) such that f(x)x-xf(x)∈Z for all invertible (singular) x∈Mn(D).

Original languageEnglish
Pages (from-to)318-324
Number of pages7
JournalLinear Algebra and Its Applications
Issue number1
Publication statusPublished - 2014 Jan 1


All Science Journal Classification (ASJC) codes

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

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