Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules
In this paper, it is shown that there exists a particular associative ring with unity of order 16 such that the relations between non-unimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of the generalized quadrangle of order two. Such...
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| Published in | Axioms Vol. 8; no. 1; p. 28 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
04.03.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2075-1680 2075-1680 |
| DOI | 10.3390/axioms8010028 |
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| Abstract | In this paper, it is shown that there exists a particular associative ring with unity of order 16 such that the relations between non-unimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of the generalized quadrangle of order two. Such a doily-centered geometric structure is surmised to be of relevance for quantum information. |
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| AbstractList | In this paper, it is shown that there exists a particular associative ring with unity of order 16 such that the relations between non-unimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of the generalized quadrangle of order two. Such a doily-centered geometric structure is surmised to be of relevance for quantum information. |
| Author | Saniga, Metod Bartnicka, Edyta |
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| Cites_doi | 10.1007/s00022-008-2090-4 10.1016/B978-044488355-1/50005-0 10.1088/0264-9381/29/22/224008 10.1142/S0219749917500265 10.1103/PhysRevD.96.026018 |
| ContentType | Journal Article |
| Copyright | 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| DOI | 10.3390/axioms8010028 |
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| References | ref_1 Saniga (ref_3) 2008; 4 ref_2 Havlicek (ref_4) 2009; 92 Holweck (ref_8) 2017; 15 Saniga (ref_5) 2007; 1 Holweck (ref_6) 2017; 96 Borsten (ref_7) 2012; 29 |
| References_xml | – volume: 92 start-page: 79 year: 2009 ident: ref_4 article-title: Vectors, Cyclic Submodules and Projective Spaces Linked with Ternions publication-title: J. Geom. doi: 10.1007/s00022-008-2090-4 – ident: ref_1 doi: 10.1016/B978-044488355-1/50005-0 – ident: ref_2 – volume: 1 start-page: 1 year: 2007 ident: ref_5 article-title: Multiple Qubits as Symplectic Polar Spaces of Order Two publication-title: Adv. Stud. Theor. Phys. – volume: 29 start-page: 224008 year: 2012 ident: ref_7 article-title: The Black-Hole/Qubit Correspondence: An Up-To-Date Review publication-title: Class. Quant. Gravity doi: 10.1088/0264-9381/29/22/224008 – volume: 15 start-page: 1750026 year: 2017 ident: ref_8 article-title: Contextuality with a Small Number of Observables publication-title: Int. J. Quant. Inf. doi: 10.1142/S0219749917500265 – volume: 96 start-page: 026018 year: 2017 ident: ref_6 article-title: Magic Three-Qubit Veldkamp Line: A Finite Geometric Underpinning for Form Theories of Gravity and Black Hole Entropy publication-title: Phys. Rev. D doi: 10.1103/PhysRevD.96.026018 – volume: 4 start-page: 50 year: 2008 ident: ref_3 article-title: Twin “Fano-Snowflakes” over the Smallest Ring of Ternions publication-title: Symmetry Integr. Geom. |
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| SubjectTerms | associative ring with unity Conflicts of interest free cyclic submodules generalized quadrangle Geometry Quantum phenomena Rings (mathematics) |
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| Title | Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules |
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