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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2005, Number 2, Pages 3–42 (Mi basm125)  
This article is cited in 10 scientific papers (total in 10 papers)

On orthogonality of binary operations and squares

Gary L. Mullena, Victor A. Shcherbacovb

a Department of Mathematics, Pennsylvania State University, University Park, USA
b Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova
Full-text PDF (340 kB) Citations (10)
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Abstract: Orthogonality of a pair of binary groupoids, left quasigroups and quasigroups from some points of view is studied. Necessary and sufficient conditions of orthogonality of a finite quasigroup and any its parastrophe (conjugate quasigroup in other terminology), including ones in language of quasi-identities, are given. New concept of gisotopy, which generalizes the concept of isotopy, is defined. There is information on quasigroups with self-orthogonal conjugates.
Keywords and phrases: Groupoid, left quasigroup, quasigroup, Latin square, row-Latin square, Latin square with self-orthogonal conjugates, orthogonality, parastrophy, isotopy, isostrophy, gisotopy.
Received: 16.07.2005
Bibliographic databases:
MSC: 20N05, 05B15, 20N02, 08C15
Language: English
Citation: Gary L. Mullen, Victor A. Shcherbacov, “On orthogonality of binary operations and squares”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, no. 2, 3–42
Citation in format AMSBIB
\Bibitem{MulShc05}
\by Gary~L.~Mullen, Victor~A.~Shcherbacov
\paper On orthogonality of binary operations and squares
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2005
\issue 2
\pages 3--42
\mathnet{http://mi.mathnet.ru/basm125}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2190736}
\zmath{https://zbmath.org/?q=an:1059.05046|1091.47029}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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