Comparing First Order Theories of Modules over Group Rings

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Mathematical Logic Quarterly 48 (1):147-156 (2002)
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Abstract

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 of all R-torsionfree RG-modules and the theory T0 of RG-lattices , 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

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10.1002/1521-3870(200201)48:1

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The decision problem for {vec Z}C(p^3)-lattices with p prime.Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):127-142.
An undecidability theorem for lattices over group rings.Carlo Toffalori - 1997 - Annals of Pure and Applied Logic 88 (2-3):241-262.

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