Abstract
In this note we study rings having only a finite number of non isomorphic uniform modules with non zero socle. It is proved that a commutative ring with this property is a direct sum of a finite ring and a ring of finite representation type. In the non commutative case we show that most P.I. rings having only a finite number of non isomorphic modules with non zero socle are in fact artinian.
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Jondrup, S., Krempa, J. & Niewieczerzal, D. A note on indecomposable modules. Rend. Circ. Mat. Palermo 37, 100–108 (1988). https://doi.org/10.1007/BF02844270
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DOI: https://doi.org/10.1007/BF02844270