Finite quadratic modules and lattices
arXiv:2110.06783 · doi:10.1080/00927872.2023.2245924
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.
33 pages