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

Puninski, G.; Toffalori, Carlo

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.

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Titolo:	Towards the decidability of the theory of modules over finite commutative rings
Autori:	PUNINSKI G. TOFFALORI, Carlo mostra contributor esterni nascondi contributor esterni
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
Appare nelle tipologie:	Articolo

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