Finitely Generated Modules over Pullback Rings Original Research Article

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. IfRis the pullback of two hereditary noetherian homogeneously serial rings, finitely generated over their centers, 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 then used as the key step in the case where the coordinate rings are hereditary noetherian serial rings over a common quotient which is a matrix ring over a field, resulting in a complete module classification.