可换环上上三角矩阵代数的若当自同构分解(英文)

Decomposition of Jordan Automorphisms of Upper Triangular Matrix Algebra over Commutative Rings

设R是含单位元1和可逆元2的可换环,Tn+1(R)表示R上(n+1)×(n+1)级上三角矩阵全体所形成的矩阵代数.本文证明了T(R)的每一个若当自同构都可唯一的分解为图自同构,内自同构和对角自同构的乘积.

Let R be a commutative ring with identity I and unit 2, Tn＋1 （R） the algebra of all upper triangular n＋1 by n＋1 matrices over R. In this article, we prove that any Jordan automorphism of Tn＋1 （R） can be uniquely written as a product of graph, inner and diagonal automorphisms.