Nonadditive strong commutativity preserving maps on rank–k matrices over division rings

Cheng Kai Liu; Pao Kuei Liau; Yuan Tsung Tsai

doi:10.7153/OAM-2018-12-35

Nonadditive strong commutativity preserving maps on rank–k matrices over division rings

Cheng Kai Liu, Pao Kuei Liau, Yuan Tsung Tsai

Department of Mathematics

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

Let M_n (픻) be the ring of all n × n matrices over a division ring 픻, wheren ≥ 2 is an integer and let S be the set of all rank-k matrices in M_n (픻), wherek is an integer with 1 ≤ k ≤ n. We characterize maps f: S → M_n (픻) such that [f (x), f (y)] = [x,y] for all x,y ∈ S.

Original language	English
Pages (from-to)	563-578
Number of pages	16
Journal	Operators and Matrices
Volume	12
Issue number	2
DOIs	https://doi.org/10.7153/OAM-2018-12-35
Publication status	Published - 2018 Jun

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory

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Liu, C. K., Liau, P. K., & Tsai, Y. T. (2018). Nonadditive strong commutativity preserving maps on rank–k matrices over division rings. Operators and Matrices, 12(2), 563-578. https://doi.org/10.7153/OAM-2018-12-35

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abstract = "Let Mn (픻) be the ring of all n × n matrices over a division ring 픻, wheren ≥ 2 is an integer and let S be the set of all rank-k matrices in Mn (픻), wherek is an integer with 1 ≤ k ≤ n. We characterize maps f: S → Mn (픻) such that [f (x), f (y)] = [x,y] for all x,y ∈ S.",

author = "Liu, {Cheng Kai} and Liau, {Pao Kuei} and Tsai, {Yuan Tsung}",

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