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On the representations of projective geometries in algebraic combinatorial geometries

✍ Scribed by DĂnuţ Marcu

Publisher
Springer
Year
1989
Tongue
English
Weight
318 KB
Volume
30
Category
Article
ISSN
0046-5755

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✦ Synopsis

In this paper, we show that the full algebraic combinatorial geometry is not a projective geometry, it is only semimodular, but the p-polynomial points give a projective subgeometry. Also, we show that the subgeometry can be coordinatized by a skew field, which is quotient ring of an Ore domain. As a corollary, we prove the existence of algebraic representations over fields of prime characteristic of the non-Pappus matroid and its dual matroid. Regarding the existence of algebraic representations of the non-Pappus matroid, this result was earlier proved by Lindstrbm [7] for finite fields.

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