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arXiv · 2110.06783

Finite quadratic modules and lattices

Xiao-Jie Zhu
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Abstract

We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For any indecomposable finite quadratic module, we construct a lattice, and a positive definite lattice, both of which are of the least rank, whose discriminant module is the given one. The resulting lattices are given by their Gram matrices explicitly.

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Xiao-Jie Zhu. 2021-10-13. Finite quadratic modules and lattices. https://doi.org/10.1080/00927872.2023.2245924

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