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Comparing First Order Theories of Modules over Group Rings II: Decidability
Author(s) -
Cittadini Saverio,
Toffalori Carlo
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200211)48:4<483::aid-malq483>3.0.co;2-s
Subject(s) - mathematics , decidability , order (exchange) , group (periodic table) , pure mathematics , dedekind cut , group ring , discrete mathematics , physics , finance , quantum mechanics , economics
We consider R ‐torsionfree modules over group rings RG , where R is a Dedekind domain and G is a finite group. In the first part of the paper [4] we compared the theory T( RG ) of all R ‐torsionfree RG ‐modules and the theory T 0 ( RG ) of RG ‐lattices (i. e. finitely generated R ‐torsionfree RG ‐modules), and we realized that they are almost always different. Now we compare their behaviour with respect to decidability, when RG ‐lattices are of finite, or wild representation type.