50 years of Finite Geometry, the 'geometries over finite rings'
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| Název: | 50 years of Finite Geometry, the 'geometries over finite rings' |
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| Autoři: | Keppens, Dirk |
| Zdroj: | Innov. Incidence Geom. 15, no. 1 (2017), 123-143 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Mathematical Sciences Publishers, 2017. |
| Rok vydání: | 2017 |
| Témata: | ring geometry, finite ring, Mathematics - Rings and Algebras, 0102 computer and information sciences, 01 natural sciences, 16Y30, 51C05, finite geometry, 51E26, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), projective plane, 16P10, 0101 mathematics, 13M05, 16Y60 |
| Popis: | Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important classes of finite rings give rise to interesting geometries. In this paper we bring together some results, scattered over the literature, concerning finite rings and plane projective geometry over such rings. It doesn't contain new material, but by collecting stuff in one place, we hope to stimulate further research in this area for at least another 50 years of Finite Geometry. |
| Druh dokumentu: | Article Other literature type |
| Popis souboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 1781-6475 |
| DOI: | 10.2140/iig.2017.15.123 |
| DOI: | 10.48550/arxiv.2003.02900 |
| Přístupová URL adresa: | https://msp.org/iig/2017/15-1/iig-v15-n1-p05-s.pdf http://arxiv.org/abs/2003.02900 https://msp.org/iig/2017/15-1/p05.xhtml https://msp.org/iig/2017/15-1/iig-v15-n1-p05-s.pdf https://ui.adsabs.harvard.edu/abs/2020arXiv200302900K/abstract https://projecteuclid.org/euclid.iig/1551323011 |
| Rights: | CC BY |
| Přístupové číslo: | edsair.doi.dedup.....8b16d4ff6059ae3c4aa9cb56466fb12b |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important classes of finite rings give rise to interesting geometries. In this paper we bring together some results, scattered over the literature, concerning finite rings and plane projective geometry over such rings. It doesn't contain new material, but by collecting stuff in one place, we hope to stimulate further research in this area for at least another 50 years of Finite Geometry. |
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| ISSN: | 17816475 |
| DOI: | 10.2140/iig.2017.15.123 |