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Matematicheskie Zametki, 1968, Volume 3, Issue 4, Pages 395–401
(Mi mzm6694)
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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.
Received: 05.05.1967
Citation:
I. Sh. o. Aliev, “Power of a set of equationally complete submanifolds of a manifold of symmetrically ternary quasigroups”, Mat. Zametki, 3:4 (1968), 395–401; Math. Notes, 3:4 (1968), 252–256
Linking options:
https://www.mathnet.ru/eng/mzm6694 https://www.mathnet.ru/eng/mzm/v3/i4/p395
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