主理想整环上对称矩阵模的保逆线性映射

Linear maps preserving inverses of matrices on symmetric matrix modules over principal ideal domains

设R是特征不为3的主理想整环,2为R中的可逆元,n和m是正整数,且n≤m。刻画了R上n阶对称矩阵模Sn(R)到R上m阶矩阵模Mm(R)上的保逆线性映射的形式。

Let R be a principal ideal domain and the characteristic of R be not 3. Assume that 2 is a unit in R. Let n and m be positive integers with n ≤m. The linear maps preserving inverses of matrices from n x n symmetric matrix modules S,,（R） onto m ×m matrix modules Mm（R） over R are described.