Generic modules of tame algebras over real closed fields

Abstract

Given a generically tame finite-dimensional algebra Λ over a real closed field, we describe the relations between the infinite families of indecomposable Λ-modules with bounded dimension and the generic Λ-modules. These are similar to those occurring for the algebraically closed field case, but the parametrizations are obtained over five particular centrally bounded principal ideal domains, instead of over rational algebras.