Comparing First Order Theories of Modules over Group Rings II: Decidability: Decidability

Mathematical Logic Quarterly 48 (4):483-498 (2002)
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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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