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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Bibliographic Details
Published inAxioms Vol. 8; no. 1; p. 28
Main Authors Saniga, Metod, Bartnicka, Edyta
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 04.03.2019
Subjects
associative ring with unity
Conflicts of interest
free cyclic submodules
generalized quadrangle
Geometry
Quantum phenomena
Rings (mathematics)
Online AccessGet full text
ISSN2075-1680
2075-1680
DOI10.3390/axioms8010028

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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Correspondence-1
content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms8010028