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arXiv · 1304.0091

Extending the Concept of Chain Geometry

Andrea Blunck·Hans Havlicek
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Abstract

We introduce the chain geometry $\Sigma(K,R)$ over a ring $R$ with a distinguished subfield $K$, thus extending the usual concept where $R$ has to be an algebra over $K$. A chain is uniquely determined by three of its points, if, and only if, the multiplicative group of $K$ is normal in the group of units of $R$. This condition is not equivalent to $R$ being a $K$-algebra. The chains through a fixed point fall into compatibility classes which allow to describe the residue at a point in terms of a family of affine spaces with a common set of points.

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Andrea Blunck, Hans Havlicek. 2013-03-30. Extending the Concept of Chain Geometry. https://doi.org/10.1023/a%3A1005260729790

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