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

I. Sh. o. Aliev

Novosibirsk State University

Abstract: 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.

UDC: 512.4

Received: 05.05.1967

 English version: Mathematical Notes, 1968, 3:4, 252–256

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