In an earlier paper
in this Journal we have shown that the integral equivalence problem for
vectors in a modular lattice L on a dyadic local field F can be determined, for
dimL≠4, 5, 6, by inspecting the numbers represented in F by the characteristic
sets which are canonically associated to the given vectors. The purpose of
this paper is to remove this dimensional restriction of L. In addition, we
shall discuss the effective determination of integral equivalences amongst
vectors as well as derive some “cancellation” results. Finally, we prove, as
expected, that this same improvement carries over in the characteristic two
situation.
