形式三角矩阵环的reduced性和正则性

Reduced and regular properties of formal triangular matrix rings

设T=A0M B是形式三角矩阵环,则T是reduced环,Von Neumann正则环,强正则环及弱正则环,当且仅当A,B是reduced环,Von Neumann正则环,强正则环及弱正则环,且M=0.

Let T=（M B^ A 0）is formal triangular matrix ring, T is respectively reduced, Von Neumann regular, strong regular and weak regular, if and only if A,B are reduced, Von Neumann regular, strong regular, weak regular, and M=0.