Finitely generated modules over pullback rings

David M. Arnold and Reinhard C. Laubenbacher

Abstract. The purpose of this paper is to outline a new approach to the
classification of finitely generated indecomposable modules over certain kinds
of pullback rings. If R is the pullback of two hereditary noetherian serial
rings over a common semi simple artinian ring, then this classification can
be divided into the classification of indecomposable artinian modules and those
modules over the coordinate rings with no non trivial artinian submodules. The
classification of the artinian modules can be reduced to the case of a finite
dimensional algebra over a semi simple ring. This approach is carried out in 
the case where the coordinate rings are hereditary noetherian serial rings over
a common quotient which is a matrix ring over a field.