Affine geometry of modules over a ring with invariant basis number (Q941911)
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scientific article; zbMATH DE number 5319723
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Affine geometry of modules over a ring with invariant basis number |
scientific article; zbMATH DE number 5319723 |
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Affine geometry of modules over a ring with invariant basis number (English)
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2 September 2008
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The fundamental theorem of affine geometry, characterizing parallelism-preserving collineations as semilinear isomorphisms, is proved for several ring geometries, defined via a free \(R\)-module over IB-rings (rings \(R\) for which in any free \(R\)-module of any rank \(n < \infty\) every generating set of \(n\) elements is a basis), in which a nontransitive parallelism relation is defined. The treatment is purely algebraic.
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affine ring geometry
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fundamental theorem of affine geometry
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modules over IBN-rings
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projective geometry
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complete lattice
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collineation
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