三角矩阵代数的倾斜模

Tilting modules over triangular matrix algebras

设R=A M0 B是三角矩阵代数,关于倾斜A-模T1,倾斜B-模T2何时能扩充为倾斜R-模的问题已有讨论.本文考察了倾斜R-模在Cokernel函子下是否还是倾斜模的问题.得到了如下结论:如果(X,Y,f)是倾斜R-模,f是单射,则Cok(y)是倾斜B-模.从而给出了单点扩张代数的倾斜模的结构.

Let R=（A AMB 0 B）be a triangular matrix algebra. The problem which tilting A-modules and tilting Bmodules can be extended to tilting R-modules has been discussed in literature. The following result is proved that if （X,Y,f）is a tilting R-module, f is the mono, then Cok（Y） is a tilting B-module. Applications to one-point extension algebras are given.