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Mat. Zametki, 1968, Volume 3, Issue 4, Pages 395–401 (Mi mz6694)  

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.

Full text: PDF file (501 kB)

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

Bibliographic databases:

UDC: 512.4
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

Citation in format AMSBIB
\Bibitem{Ali68}
\by I.~Sh.~o.~Aliev
\paper Power of a~set of equationally complete submanifolds of a~manifold of symmetrically ternary quasigroups
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 4
\pages 395--401
\mathnet{http://mi.mathnet.ru/mz6694}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=225917}
\zmath{https://zbmath.org/?q=an:0185.04303}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 4
\pages 252--256
\crossref{https://doi.org/10.1007/BF01159940}


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