Power commuting additive maps on invertible or singular matrices

Cheng Kai Liu; Jheng Jie Yang

doi:10.1016/j.laa.2017.04.038

Power commuting additive maps on invertible or singular matrices

Cheng Kai Liu, Jheng Jie Yang

Department of Mathematics

Research output: Contribution to journal › Article

6 Citations (Scopus)

Abstract

Let F be a field and let M_n(F) be the ring of all n×n matrices over F, where n≥2 is an integer. We characterize additive maps f:M_n(F)→M_n(F) satisfying f(x)x^m=x^mf(x) for all invertible (singular) x∈M_n(F), where m≥2 is an integer.

Original language	English
Pages (from-to)	127-149
Number of pages	23
Journal	Linear Algebra and Its Applications
Volume	530
DOIs	https://doi.org/10.1016/j.laa.2017.04.038
Publication status	Published - 2017 Oct 1

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All Science Journal Classification (ASJC) codes

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

Cite this

Liu, C. K., & Yang, J. J. (2017). Power commuting additive maps on invertible or singular matrices. Linear Algebra and Its Applications, 530, 127-149. https://doi.org/10.1016/j.laa.2017.04.038

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AB - Let F be a field and let Mn(F) be the ring of all n×n matrices over F, where n≥2 is an integer. We characterize additive maps f:Mn(F)→Mn(F) satisfying f(x)xm=xmf(x) for all invertible (singular) x∈Mn(F), where m≥2 is an integer.

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Access to Document

10.1016/j.laa.2017.04.038