IMCS/Publications/BASM/Issues/BASM n.1 (20), 1996/

On D-groupoids, quasigroups and homomorphisms. (English)

Authors: Izbaş Vladimir, Prodan N.


In this paper it is proved that there exists a $D$-groupoid $Q(\cdot )$ and systems of identities $\Sigma $ such that $Q(\cdot )$ can not be represented as a homomorphic image of a quasigroup $G(\circ )$ if $Q(\cdot )$ and $G(\circ )$ satisfy the identities of $\Sigma $. Also the smallest sub@-$D$@-groupoid $K$ is constructed such that $Q/K(\ast )$ is a group.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău, MD-2028 Moldova