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

被引：3

作者：

Puninski, Gena ^{[2
]}

Toffalori, Carlo ^{[1
]}

机构：

[1] Univ Camerino, Dept Math & Informat, I-62032 Camerino, Italy

[2] Univ Manchester, Dept Math, Manchester M13 9PL, Lancs, England

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2009年 / 159卷 / 1-2期

关键词：

Theory of modules; Decidability; Finite commutative ring; Ziegler spectrum; Klingler-Levy classification; REPRESENTATION TYPE; STRING ALGEBRAS; KRULL DIMENSION; ZIEGLER; SPECTRA;

D O I：

10.1016/j.apal.2008.10.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 a decidable theory of modules. We prove that if R is (finite length) wild, then the theory of all R-modules is undecidable, and verify clecidability of this theory for some classes of tame finite commutative rings. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：49 / 70

页数：22

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