Adjacency preserving bijective maps on triangular matrices over any division ring |
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| Authors: | Li-Ping Huang |
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| Affiliation: | 1. School of Mathematics and Computing Science , Changsha University of Science and Technology , Changsha 410076, P. R. China lipingmath@sohu.com |
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| Abstract: | Let 𝕋 n (D) be the set of n × n upper triangular matrices over a division ring D. We characterize the adjacency preserving bijective maps in both directions on 𝕋 n (D) (n ≥ 3). As applications, we describe the ring semi-automorphisms and the Jordan automorphisms on upper triangular matrices over a simple Artinian ring. |
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| Keywords: | triangular matrices adjacency geometry of matrices semi-automorphism simple Artinian ring |
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