A Jacobson Radical Decomposition of the Fano-Snowflake Configuration
The Fano-Snowflake, a specific configuration associated with the smallest ring of ternions Rà (arXiv:0803.4436 and arXiv:0806.3153), admits an interesting partitioning with respect to the Jacobson radical of Rà. The totality of 21 free cyclic submodules generated by non-unimodular vectors of the fre...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149008 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Jacobson Radical Decomposition of the Fano-Snowflake Configuration / M. Saniga, P. Pracna // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | The Fano-Snowflake, a specific configuration associated with the smallest ring of ternions Rà (arXiv:0803.4436 and arXiv:0806.3153), admits an interesting partitioning with respect to the Jacobson radical of Rà. The totality of 21 free cyclic submodules generated by non-unimodular vectors of the free left Rà-module Rà³ is shown to split into three disjoint sets of cardinalities 9, 9 and 3 according as the number of Jacobson radical entries in the generating vector is 2, 1 or 0, respectively. The corresponding ''ternion-induced'' factorization of the lines of the Fano plane sitting in the middle of the Fano-Snowflake is found to differ fundamentally from the natural one, i.e., from that with respect to the Jacobson radical of the Galois field of two elements.
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| ISSN: | 1815-0659 |