Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2007, Number 2, Pages 43–54 (Mi basm61)  
This article is cited in 3 scientific papers (total in 3 papers)

On definitions of groupoids closely connected with quasigroups

V. A. Shcherbacov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
Full-text PDF (139 kB) Citations (3)
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Abstract: Both “existential” and “equational” definitions of binary quasigroups and groupoids closely connected with quasigroups are given. It is proved that a groupoid $(Q,\cdot)$ is a quasigroup if and only if all middle translations of $(Q,\cdot)$ are bijective maps of the set $Q$.
Keywords and phrases: Quasigroup, left quasigroup, right quasigroup, division groupoid, cancellation groupoid, translation.
Received: 26.06.2007
Bibliographic databases:
MSC: 20N05
Language: English
Citation: V. A. Shcherbacov, “On definitions of groupoids closely connected with quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2007, no. 2, 43–54
Citation in format AMSBIB
\Bibitem{Shc07}
\by V.~A.~Shcherbacov
\paper On definitions of groupoids closely connected with quasigroups
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2007
\issue 2
\pages 43--54
\mathnet{http://mi.mathnet.ru/basm61}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2343129}
\zmath{https://zbmath.org/?q=an:1176.20065}
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  • https://www.mathnet.ru/eng/basm/y2007/i2/p43
    • This publication is cited in the following 3 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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