Shcherbacov, V. A. On definitions of groupoids closely connected with quasigroups. (English) Zbl 1176.20065 Bul. Acad. Ştiinţe Repub. Mold., Mat. 2007, No. 2(54), 43-54 (2007). Summary: 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 \(Q\). Cited in 3 Documents MSC: 20N05 Loops, quasigroups 20N02 Sets with a single binary operation (groupoids) Keywords:quasigroups; groupoids; translations PDFBibTeX XMLCite \textit{V. A. Shcherbacov}, Bul. Acad. Științe Repub. Mold., Mat. 2007, No. 2(54), 43--54 (2007; Zbl 1176.20065)