Power of a~set of equationally complete submanifolds of a~manifold of symmetrically ternary quasigroups

I. Sh. o. Aliev

Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 395-401.

Résumé

Manifolds of algebras with the operation $xyz\tau$ defined by the following identities: 1) $xyz\tau yz\tau=x$; 2)$xxyz\tau z\tau=y$; 3) $xyxyz\tau\tau=z$; 4) $xxz\tau=z$, which correspond to Steiner quadruplets [3], like manifolds of structures, have a unique equationally complete submanifold [4]. It is proved that in the class of all algebras defined only by the identities 1), 2), and 3) the set of all equationally complete submanifolds has the power of a continuum.