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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2005, Number 2, Pages 3–42
(Mi basm125)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/basm125 https://www.mathnet.ru/eng/basm/y2005/i2/p3
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