On distant-isomorphisms of projective lines
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| Title: | On distant-isomorphisms of projective lines |
|---|---|
| Authors: | Hans Havlicek, Andrea Blunck |
| Source: | Aequationes mathematicae. 69:146-163 |
| Publication Status: | Preprint |
| Publisher Information: | Springer Science and Business Media LLC, 2005. |
| Publication Year: | 2005 |
| Subject Terms: | Mathematics - Algebraic Geometry, 51C05, 51A10, 51A45, 17C50, Incidence structures embeddable into projective geometries, Homomorphism, automorphism and dualities in linear incidence geometry, Rings and Algebras (math.RA), Ring geometry (Hjelmslev, Barbilian, etc.), Jordan structures associated with other structures, FOS: Mathematics, Mathematics - Rings and Algebras, 0101 mathematics, projective line over a ring, Algebraic Geometry (math.AG), 01 natural sciences |
| Description: | We determine all distant-isomorphisms between projective lines over semilocal rings. In particular, for those semisimple rings that do not have a simple component which is isomorphic to a field, every distant isomorphism arises from a Jordan isomorphism of rings and a projectivity. We show this by virtue of a one-one correspondence linking the projective line over a semisimple ring with a Segre product of Grassmann spaces. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1420-8903 0001-9054 |
| DOI: | 10.1007/s00010-004-2745-7 |
| DOI: | 10.48550/arxiv.1304.0226 |
| Access URL: | http://arxiv.org/pdf/1304.0226 http://arxiv.org/abs/1304.0226 https://documat.unirioja.es/servlet/articulo?codigo=2204366 https://rd.springer.com/article/10.1007/s00010-004-2745-7 https://link.springer.com/article/10.1007/s00010-004-2745-7 https://dialnet.unirioja.es/servlet/articulo?codigo=2204366 https://link.springer.com/10.1007/s00010-004-2745-7 |
| Rights: | Springer TDM arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....322767c8af2e0443b4806d2cfbcc56f1 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | We determine all distant-isomorphisms between projective lines over semilocal rings. In particular, for those semisimple rings that do not have a simple component which is isomorphic to a field, every distant isomorphism arises from a Jordan isomorphism of rings and a projectivity. We show this by virtue of a one-one correspondence linking the projective line over a semisimple ring with a Segre product of Grassmann spaces. |
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| ISSN: | 14208903 00019054 |
| DOI: | 10.1007/s00010-004-2745-7 |