主理想整环上保对合矩阵的线性映射

LINEAR MAPS PRESERVING INVOLUTORY MATRICES OVER PRINCIPAL IDEAL DOMAINS

设 R是特征不为 2的交换主理想整环 ,Mn( R)表示 R上 n阶全矩阵模 ,本文使用基底生成元的方法刻划 Mn( R)上保对合矩阵的

Let R be a commutative principal ideal domain of characteristic not 2, and let Mn(R) is the n×n matrix module over R . We determine the forms of R linear maps, from M n(R) to M n(R) , which preserve involutory matrices by using the methold of generating element of the basis.