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On the geometry of field extensions. (English) Zbl 0787.51006

Let \(L\) be a field extension over \(K\). In the case where \(K\) is a part of the centre \(L\) such concepts as spread and chains were investigated. In this paper the author investigates the case when \(K\) is not a part of the centre of \(L\).
The main tool in this paper is the concept of transversal lines of a chain. With the help of this notion the author gives a simple geometric proof of the Cartan-Brauer-Hua theorem.
A crucial result of this paper is the geometric description of the spread and chain by means of collineations.
Reviewer: M.Uscki (Toruń)

MSC:

51B10 Möbius geometries
51A25 Algebraization in linear incidence geometry
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References:

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