Vol. 31, No. 1, 1969

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Integral equivalence of vectors over local modular lattices. II

John Sollion Hsia

Vol. 31 (1969), No. 1, 47–59

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 dimL4, 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.

Mathematical Subject Classification
Primary: 15.70
Received: 27 November 1968
Published: 1 October 1969
John Sollion Hsia