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
收藏
页码：49 / 70
页数：22
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