三角矩阵环上FC-投射模的刻画

A characterization of FC-projective modules over triangular matrix rings

设T=(A 0 U B)是形式三角矩阵环,其中A,B是环,U是(B,A)-双模.给出了有限余生成左T-模和有限余表示左T-模在形式三角矩阵环上的等价刻画,进而给出了形式三角矩阵环T上FC-投射左T-模的刻画.作为应用,讨论了左T-模的FC-投射维数.

Let T=(A 0 U B) be a formal triangular matrix ring,where A and B are rings and U is a(B,A)-bimodule.Equivalent characterizations of left T-modules of finite cogeneration and finite corepresentation on the formal triangular matrix ring are given.Furthermore,a characterization of FC-projective left T-modules over the formal triangular matrix ring is given.As an application,the FC-projective dimensions of left T-modules are discussed.