On definitions of groupoids closely connected with quasigroups
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SHCHERBACOV, Victor. On definitions of groupoids closely connected with quasigroups. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2007, nr. 2(54), pp. 43-54. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(54) / 2007 / ISSN 1024-7696 /ISSNe 2587-4322

On definitions of groupoids closely connected with quasigroups

Pag. 43-54

Shcherbacov Victor
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 7 decembrie 2013


Rezumat

Both “existential” and “equational” definitions of binary quasigroups and groupoids closely connected with quasigroups are given. It is proved that a groupoid (Q, ·) is a quasigroup if and only if all middle translations of (Q, ·) are bijective maps of the set Q.

Cuvinte-cheie
quasigroup, cancellation groupoid,

left quasigroup, right quasigroup, division groupoid