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A Jacobson Radical Decomposition of the Fano-Snowflake Configuration
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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| dc.contributor.author | Saniga, M. | |
| dc.contributor.author | Pracna, P. | |
| dc.date.accessioned | 2019-02-19T12:55:50Z | |
| dc.date.available | 2019-02-19T12:55:50Z | |
| dc.date.issued | 2008 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2000 Mathematics Subject Classification: 51C05; 51Exx | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/149008 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | The work was partially supported by the VEGA grant agency projects Nos. 6070 and 7012, the CNRS-SAV Project No. 20246 and by the Action Austria–Slovakia project No. 58s2. We thank Hans Havlicek (Vienna University of Technology) for valuable comments and suggestions. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | A Jacobson Radical Decomposition of the Fano-Snowflake Configuration | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
