Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings
type: Item
instance of: scholarly article
title: Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings
zbMATH Open document ID: 1048.11029
published in: Archiv der Mathematik
publication date: 2004-03-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11E08
zbMATH DE Number: 2051618
zbMATH Keywords: modular lattice
zbMATH Keywords: minimal norm Jordan splittings
zbMATH Keywords: Witt cancellation
zbMATH Keywords: lattice
zbMATH Keywords: classification of lattices
author: Fei Xu
reviewed by: Kazimierz Szymiczek
MaRDI profile type: Publication
full work available at URL: s00013-003-4627-y
OpenAlex ID: W2013246626
DOI: 10.1007/S00013-003-4627-Y
description: scientific article; zbMATH DE number 2051618