Indecomposable quadratic lattices over global function fields
If \(V\) is a regular quadratic space over a global function field \(F\) whose characteristic is not 2, then \(L \subseteq V\) is a \(o\)-lattice if it is a \(o\)-module with \(FL=V\) where \(o\) is the Hasse domain of \(F\). If there do not exist sublattices with \(L_1 \perp L_2 = L\) then \(L\) is said to be indecomposable. The author proves that there exists an indecomposable lattice of rank 5 over a Hasse domain of any rational function field for which \(-1\) is not a square. Examples of three indecomposable lattices of rank 5 and 6 over a Hasse domain of \(F_7(x)\) are also given.
scientific article; zbMATH DE number 6516882