On the geometry of field extensions (Q1801342)
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scientific article; zbMATH DE number 202385
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the geometry of field extensions |
scientific article; zbMATH DE number 202385 |
Statements
On the geometry of field extensions (English)
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15 May 1994
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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.
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chain geometry
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spread
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transversal lines
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collineations
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