Le théorème de Hua pour les algèbres artiniennes simples

✍ Scribed by H. Essannouni; A. Kaidi

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 141 KB
• Volume: 297
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00081-6

✦ Synopsis

Let D be a division ring and w n h be the ring of the n  n matrices with entries in D. Consider a surjective mapping r X w n h 3 w n h satisfying re f re rf for all eY f P w n hY r1 1 and for all invertible A in w n hY re is invertible and re À1 re À1 . If n 1 the well-known Hua's theorem states that r is an automorphism or an anti-automorphism. We show that if h T F 2 (the ®eld of two elements) then r is an automorphism or an anti-automorphism for all n.