Le théorème de Hua pour les algèbres artiniennes simples Original Research Article

Let D be a division ring and Mn(D) be the ring of the n×n matrices with entries in D. Consider a surjective mapping σ : Mn(D)→Mn(D) satisfying σ(A+B)=σ(A)+σ(B) for all A,Bset membership, variantMn(D), σ(1)=1 and for all invertible A in Mn(D), σ(A) is invertible and σ(A−1)=σ(A)−1. If n=1 the well-known Huaʹs theorem states that σ is an automorphism or an anti-automorphism. We show that if image (the field of two elements) then σ is an automorphism or an anti-automorphism for all n.