Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings

doi:10.1007/s00013-003-4627-y

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	Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings
	Xu, F
	2003-10-01
发表期刊	ARCHIV DER MATHEMATIK
ISSN	0003-889X
卷号	81 期号:4 页码:402-415
摘要	In [5], the so called minimal norm Jordan splitting over a ring of integers of dyadic local fields is introduced for determining the generators of integral orthogonal groups for the purpose of computing integral spinor norms. Such a normalization of Jordan splittings turns out to be useful in dyadic theory (see also [6] and [7]). In this note, we give a more conceptual proof and extend this result to a complete dyadic discrete valuation ring, where the residue field is not necessarily perfect. As an application, we discuss the Witt cancellation theorem and also give a proof of Theorem 10 in [4, Chapter 10], where the rigorous proof is not available. It should be pointed out that [31 gives some variation of the classification theorem over Z(2) but not the detailed proof.
DOI	10.1007/s00013-003-4627-y
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000187109000005
出版者	BIRKHAUSER VERLAG AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18816
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, F
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Xu, F. Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings[J]. ARCHIV DER MATHEMATIK,2003,81(4):402-415.
APA	Xu, F.(2003).Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings.ARCHIV DER MATHEMATIK,81(4),402-415.
MLA	Xu, F."Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings".ARCHIV DER MATHEMATIK 81.4(2003):402-415.