Vol. 23, No. 3, 1967

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ISSN: 0030-8730
Integral equivalence of vectors over local modular lattices

John Sollion Hsia

Vol. 23 (1967), No. 3, 527–542
Abstract

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 subgroup

0(L) = {σ ∈ 0(V)|σL = L}

of the orthogonal group 0(V ). Two vectors u and v in L are defined to be integrally equivalent if there exists an isometry σ 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.

Mathematical Subject Classification
Primary: 15.70
Milestones
Received: 31 January 1967
Revised: 2 April 1967
Published: 1 December 1967
Authors
John Sollion Hsia