Zhao （2003a） first established a congruence for any odd prime p〉3, S（1,1,1 ;p）=-2Bp-3 （mod p）, which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S（α,β, γ,ρ） （modp） is considered for all positive integers α,β, γ. We refer to w=α＋β＋ γ as the weight of the sum, and show that if w is even, S（α,β, γ,ρ）=0 （mod p） for p≥w＋3; if w is odd, S（α,β, γ,ρ）=-rBp-w （mod p） for p≥w, here r is an explicit rational number independent ofp. A congruence of Catalan number is obtained as a special case.
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.
