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Axioms 2019, 8(1), 28; https://doi.org/10.3390/axioms8010028

Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules

1
Astronomical Institute of the Slovak Academy of Sciences, SK-05960 Tatranská Lomnica, Slovakia
2
Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54 Street, P-10710 Olsztyn, Poland
*
Author to whom correspondence should be addressed.
Received: 31 January 2019 / Revised: 28 February 2019 / Accepted: 2 March 2019 / Published: 4 March 2019
(This article belongs to the Special Issue Foundations of Quantum Computing)
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PDF [374 KB, uploaded 7 March 2019]
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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. View Full-Text
Keywords: associative ring with unity; free cyclic submodules; generalized quadrangle associative ring with unity; free cyclic submodules; generalized quadrangle
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Saniga, M.; Bartnicka, E. Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules. Axioms 2019, 8, 28.

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