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Finitely Generated Modules over Pullback Rings

✍ Scribed by David M. Arnold; Reinhard C. Laubenbacher

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 273 KB
Volume: 184
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0262

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✦ Synopsis

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 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.

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