An undecidability theorem for lattices over group rings

Annals of Pure and Applied Logic 88 (2-3):241-262 (1997)
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Abstract

Let G be a finite group, T denote the theory of Z[G]-lattices . It is shown that T is undecidable when there are a prime p and a p-subgroup S of G such that S is cyclic of order p4, or p is odd and S is non-cyclic of order p2, or p = 2 and S is a non-cyclic abelian group of order 8 . More precisely, first we prove that T is undecidable because it interprets the word problem for finite groups; then we lift undecidability from T to T

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References found in this work

Model theory of modules.Martin Ziegler - 1984 - Annals of Pure and Applied Logic 26 (2):149-213.
The theory of {vec Z}C(2)^2-lattices is decidable.Stefano Baratella & Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):91-104.
The elementary theory of abelian groups.Paul C. Eklof - 1972 - Annals of Mathematical Logic 4 (2):115.
Model Theory and Modules.Mike Prest - 1989 - Journal of Symbolic Logic 54 (3):1115-1118.
Elementary Properties of Abelian Groups.W. Szmielew - 1959 - Journal of Symbolic Logic 24 (1):59-59.

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