Divisorial Ideals in the Power Series Ring A+XB[[X]]

Let A⊆ B be an extension of integral domains, B[[X]] be the power series ring over B, and R=A + XB[[X]] be a subring of B[[X]]. In this paper, we give a complete description of v-invertible v-ideals (with nonzero trace in A) of R. We show that if B is a completely integrally closed domain and I is a fractional divisorial v-invertible ideal of R with nonzero trace over A, then I = u(J_1 + XJ_2[[X]]) for some u∈ qf(R), J_2 an integral divisorial v-invertible ideal of B and J_1⊆ J_2 a nonzero ideal of A.