This article is cited 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

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.

MSC: 20N05

Received: 26.06.2007

Language: English

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