MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 103

Preprint Number 103

Previous Next Preprint server


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

Submission date: 21 November 2007

Abstract:

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

Full text: pdf, dvi, ps.


Last updated: October 20 2009 12:55 Please send your corrections to: