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Preprint Number 103

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103. Gena Puninski, Carlo Toffalori
Towards the decidability of the theory of modules over finite commutative rings

Submission date: 21 November 2007


On the basis of the Klingler-Levy classification of finitely generated modules over commutative noetherian rings we approach the old problem of classifying finite commutative rings R with decidable theory of modules. We prove that if R is (finite length) wild, then the theory of all R-modules is undecidable, and verify decidability of this theory for some classes of tame finite commutative rings.

Mathematics Subject Classification: 03C60, 03B25, 16D50, 16P10, 16G60

Keywords and phrases: Theory of modules, Decidability, Finite commutative ring, Ziegler spectrum, Klingler-Levy classification

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