摘要
In this paper we carry out a study of modules over a 3 × 3 formal triangular matrix ringГ=（T 0 0 M U 0 N×UM N V）where T, U, V are rings, M, N are U-T, V-U bimodules, respectively. Using the alternative description of left Г-module as quintuple （A, B, C; f, g） with A ∈ mod T, B ∈ mod U and C ∈ mod V, f ： M ×T A →B ∈ mod U, g ： N ×U B → C ∈ mod V, we shall characterize uniform, hollow and finitely embedded modules over F, respectively. Also the radical as well as the socle of r （A ＋ B ＋ C） is determined.
In this paper we carry out a study of modules over a 3×3 formal triangular matrix ring ■ where T,U,V are rings,M,N are U-T,V-U bimodules,respectively.Using the alternative description of left r-module as quintuple(A,B,C;f,g)with A∈modT,B∈modU and C∈modV,f:M_T A→B∈modU,g:N_U B→C∈modV,we shall characterize uniform,hollow and finitely embedded modules overΓ,respectively.Also the radical as well as the socle of r(A⊕B⊕C)is determined.
基金
the National Natural Science Foundation of China （No. 10371107）.
