Centralizing maps on invertible or singular matrices over division rings

作者：Liu Cheng Kai^*

来源：Linear Algebra and Its Applications, 2014, 440: 318-324.

DOI：10.1016/j.laa.2013.10.016

• Centralizing maps
• Functional identities
• Invertible matrices
• Singular matrices

Let D be a division ring and let M-n(D) be the ring of all n x 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) is an element of Z for all invertible (singular) x is an element of M-n(D).

• 出版日期2014-1-1