Towards the decidability of the theory of modules over finite commutative rings

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 the 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.

Towards the decidability of the theory of modules over finite commutative rings / PUNINSKI G.; TOFFALORI C.. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 159:1-2(2009), pp. 49-70.



Titolo: Towards the decidability of the theory of modules over finite commutative rings
Autori: 
TOFFALORI, Carlo
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Data di pubblicazione: 2009
Rivista: 
ANNALS OF PURE AND APPLIED LOGIC  
Citazione: Towards the decidability of the theory of modules over finite commutative rings / PUNINSKI G.; TOFFALORI C.. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 159:1-2(2009), pp. 49-70.
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 the 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.
Handle: http://hdl.handle.net/11581/115121
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