Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings
In an earlier paper the author introduced minimal norm Jordan splitting of lattices over the integers in dyadic local fields [Pac. J. Math. 167, 385--398 (1995; Zbl 0829.11021)]. In the present paper he extends the results to the case of general complete dyadic discrete valuation rings. As an application he proves a version of the Witt cancellation theorem for reduced lattices. He also gives a proof for the classification theorem for lattices over dyadic integers stated without a formal proof in the book by \textit{J. H. Conway} and \textit{N. J. A. Sloane} [Sphere packings, lattices and groups. (Grundlehren der Mathematischen Wissenschaften, 290. New York: Springer-Verlag) (1988; Zbl 0634.52002)]. This is Theorem 10 in Chapter 15 of the book. Conway and Sloane, instead of engaging into the proof, say that ``it is often simpler to use the following ideas''. And they go on to compartments and trains, oddity fusion, sign walking, etc.
scientific article; zbMATH DE number 2051618