形式三角矩阵环上的模的结构

ON THE STRUCTURE OF MODULES OVER FORMAL TRIANGULAR MATRIX RINGS

利用形式三角矩阵环T上的 (右 )模的分解 ,研究右T -模的结构 ,得到一个右T -模有合成列的充分必要条件 ,以及在这一条件下 ,其合成长度的计算公式 .此外还给出形式三角矩阵环T是Max -环的一个等价刻画 .

By the decompostition of the (right) modules over the formal triangular matrix ring T, we study the structure of right T-modules.We obtain a sufficient and necessary condition under which a right T-module has a conposition series, moreover,when such a condition holds,we get a formula for calculating the composition length of the right T-module. In addition, we give an eguivalent characterization for a formal triangular matrix ring to be a Max-ring.