可换环上一类可解若当矩阵代数的若当自同构(英文)

Jordan Automorphisms of a Class of Solvable Jordan Matrix Algebras over Commutative Rings

令R表示含单位元的可换环,2是R的可逆元,■表示R上的一个可解若当矩阵代数.研究了■的若当自同构,通过归化的思想将■上的问题转化为严格上三角若当矩阵代数上的问题.最后通过构造■的四种若当自同构证明了当n≥3时,■的任何一个若当自同构均可以分解为这四种若当自同构的乘积.这个结果推广了王兴涛的的关于严格上三角矩阵代数的若当自同构分解的结果.

Let R be a commutative ring with identity and assume that 2 is a unit, y be a solvable Jordan matrix algebra over R.The Jordan automorphisms of y are studied.The problem on y is reduced to that on strictly upper triangular matrix algebra.By constructing four types of Jordan automorphisms of y,it is proved that any Jordan automorphism of y can be decomposed as a product of such four types of Jordan automorphisms for n≥3.This extends a result given by Wang Xingtao who described the decomposition of Jordan automorphisms of strictly upper triangular matrix algebra over R.