A note on deformations of finite dimensional modules over k-algebras

Let k be a field, and let Lambda be a (not necessarily finite dimensional) k-algebra. Let V be an indecomposable left Lambda-module which is finite dimensional over k and such that dim(k) Ext(Lambda)(1)(V, V) <= 1. Assume further that V has aweak universal deformation ring R-w(Lambda, V), which is a complete Noetherian commutative local k-algebra with residue field k. We prove in this note, under certain conditions on the Lambda-module V, that R-w(Lambda, V) is either isomorphic to k, or k[[t]], or to k[[t]]/(t(N)) for some integer N >= 2.