The decision problem for {vec Z}C(p^3)-lattices with p prime

Archive for Mathematical Logic 37 (2):127-142 (1998)
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Abstract

We show undecidability for lattices over a group ring ${\vec Z} \, G$ where $G$ has a cyclic subgroup of order $p^3$ for some odd prime $p$ . Then we discuss the decision problem for ${\vec Z} \, G$ -lattices where $G$ is a cyclic group of order 8, and we point out that a positive answer implies – in some sense – the solution of the “wild $\Leftrightarrow$ undecidable” conjecture

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