Baer ordered *-fields of the first kind
type: Item
instance of: scholarly article
title: Baer ordered *-fields of the first kind
zbMATH Open document ID: 0671.16008
DOI: 10.1007/BF02766220
author: Samuel S. jun. Holland
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A skew field K with an involution \(a\mapsto a^*\) (we shall shortly say a *-field) of characteristic \(\neq 2\) will be called of the first kind, if all of its central elements are symmetric \((=\) self-adjoint). It is well known that the dimension of such a field over its center is \(4^ n\) for some natural number n. In this paper, the author considers *-fields with a ``Baer ordering''. Such an ordering is given by a set P of symmetric elements with the following properties: (i) P contains 1 but not 0, (ii) \(P+P\subseteq P\), (iii) \(bPb^*\subseteq P\) for all \(b\neq 0\), (iv) \(P\cap -P=\emptyset\), (v) every symmetric element different from 0 belongs to P or -P. In this paper the author constructs Baer ordered *- fields of the first kind of dimension \(4^ n\) over their center for every natural number n. The construction is explicit and relies on earlier work of \textit{L. H. Rowen} [cf.: Isr. J. Math. 29, 285-301 (1978; Zbl 0392.16011)].
reviewed by: Klaus Keimel
Mathematics Subject Classification ID: 16Kxx
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 12J15
zbMATH DE Number: 4097573
zbMATH Keywords: skew field with involution
zbMATH Keywords: central elements
zbMATH Keywords: symmetric elements
zbMATH Keywords: Baer ordered *-fields
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4097573