Integral equivalence of vectors over local modular lattices
John S. Hsia · Pacific Journal of Mathematics · 1967
Let F be a local field with characteristic unequal to two, and in which the element 2 is not unitary.Let V be a regular quadratic space over F, L a lattice on V.The group of units of L is the subgroupof the orthogonal group 0(V).Two vectors u and v in L are defined to be integrally equivalent if there exists an isometry a e 0(L) mapping one onto the other.This paper gives necessary and sufficient conditions for integral equivalence of vectors when the underlying lattice L is modular.