Representations of a k-algebra over the rational functions over k

For Λ a finite-dimensional k-algebra, k a field, we study the relations between the category of all left Λ-modules, ModΛ, and the category of finitely generated Λ kk(x)=Λk(x)-modules, modΛk(x). In particular, we consider those G modΛk(x) such that ΛG is indecomposable. We prove that such modules are in the mouth of components in modΛk(x) which are tubes or have the shape , , or .