Let A be a subalgebra of U q (sl(2)) generated by K,K −1 and F and A δ be a subalgebra of U q (sl(2)) generated by K,K −1 (and also F d if q is a primitive d-th root of unity with d an odd number). Given an A δ -module M, a U q (sl(2))-module $$A \otimes _{A^\delta } M$$ is constructed via the iterated Ore extension of U q (sl(2)) in a unified framework for any q. Then all the submodules of $$A \otimes _{A^\delta } M$$ are determined for a fixed finite-dimensional indecomposable A δ -module M. It turns out that for some indecomposable A δ -module M, the U q (sl(2))-module $$A \otimes _{A^\delta } M$$ is indecomposable, which is not in the BGG-categories O q associated with quantum groups in general.