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
TOFFALORI, Carlo
2009-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
