Decidability for ℤ2G‐lattices when G Extends the Noncyclic Group of Order 4

Mathematical Logic Quarterly 48 (2):203-212 (2002)
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Abstract

Let G be the direct sum of the noncyclic groupof order four and a cyclic groupwhoseorderisthe power pn of some prime p. We show that ℤ2G-lattices have a decidable theory when the cyclotomic polynomia equation image is irreducible modulo 2ℤ for every j ≤ n. More generally we discuss the decision problem for ℤ2G-lattices when G is a finite group whose Sylow 2-subgroups are isomorphic to the noncyclic group of order four

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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.
The theory of {vec Z}C(2)^2-lattices is decidable.Stefano Baratella & Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):91-104.
An undecidability theorem for lattices over group rings.Carlo Toffalori - 1997 - Annals of Pure and Applied Logic 88 (2-3):241-262.
Wildness implies undecidability for lattices over group rings.Carlo Toffalori - 1997 - Journal of Symbolic Logic 62 (4):1429-1447.

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