Reguli and chains over skew fields
type: Item
instance of: scholarly article
title: Reguli and chains over skew fields
zbMATH Open document ID: 0952.51002
author: Andrea Blunck
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/120708
full work available at URL: BAG
review text: The author gives a new geometric definition of a regulus in a not necessarily pappian projective space \(PG(V,K)\) of arbitrary dimension. She proves that any three mutually complementary subspaces are contained in a regulus, which is unique precisely if the skew field \(K\) is commutative. Furthermore, these reguli have an interpretation in chain geometry [compare the author, Bull. Belg. Math. Soc. Simon Stevin 6, No. 4, 589-603 (1999)] and \textit{W. Benz} [`Vorlesungen über Geometrie der Algebren', Springer Verlag, Berlin (1973; Zbl 0258.50024)]: there is a natural bijection which maps reguli onto the chains of the projective line over the ring \(R=\text{End}_K (U)\), where \(U\oplus U\cong V\).
Mathematics Subject Classification ID: 51A30
Mathematics Subject Classification ID: 51B05
zbMATH DE Number: 1428657
zbMATH Keywords: regulus
zbMATH Keywords: chain geometry
reviewed by: Theo Grundhöfer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1428657