Geometry of free cyclic submodules over ternions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2010
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| Acceso en línea: | |
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| _version_ | 1866916122379419648 |
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| author | Havlicek, Hans Matras, Andrzej Pankov, Mark |
| author_facet | Havlicek, Hans Matras, Andrzej Pankov, Mark |
| contents | Given the algebra $T$ of ternions (upper triangular $2\times 2$ matrices) over a commutative field $F$ we consider as set of points of a projective line over $T$ the set of all free cyclic submodules of $T^2$. This set of points can be represented as a set of planes in the projective space over $F^6$. We exhibit this model, its adjacency relation, and its automorphic collineations. Despite the fact that $T$ admits an $F$-linear antiautomorphism, the plane model of our projective line does not admit any duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1012_1459 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Geometry of free cyclic submodules over ternions Havlicek, Hans Matras, Andrzej Pankov, Mark Rings and Algebras Combinatorics Given the algebra $T$ of ternions (upper triangular $2\times 2$ matrices) over a commutative field $F$ we consider as set of points of a projective line over $T$ the set of all free cyclic submodules of $T^2$. This set of points can be represented as a set of planes in the projective space over $F^6$. We exhibit this model, its adjacency relation, and its automorphic collineations. Despite the fact that $T$ admits an $F$-linear antiautomorphism, the plane model of our projective line does not admit any duality. |
| title | Geometry of free cyclic submodules over ternions |
| topic | Rings and Algebras Combinatorics |
| url | https://arxiv.org/abs/1012.1459 |