主理想整环上对称矩阵的非结合代数自同构

摘要

本文研究了一类非结合代数的自同构.利用分式化方法,得到主理想整环上对称矩阵构成的非结合代数的所有自同构形式,并刻画了相应的Jordan自同构.%In this paper, we study the automorphism of a type of non-associative algebra. By using the fraction method, we obtain the forms of all automorphisms of the non-associate algebra consisting of symmtric matrices over a PID. The corresponding Jordan automorphisms are also characterized.