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On the variety generated by Murskiĭ’s algebra. (English) Zbl 0542.08004
Let \(M\) be V. L. Murskiĭ ’s finite algebra [Sov. Math., Dokl. 6, 1020–1024 (1965); translation from Dokl. Akad. Nauk SSSR 163, 815–818 (1965; Zbl 0154.25506)] and \(\mathrm{var}\,M\) the variety generated by \(M\). In previous papers of the author it was shown that \(\mathrm{var}\,M\) has neither DCC nor ACC. The present paper shows that \(\mathrm{var}\,M\) has uncountably many subvarieties.

MSC:
08B15 Lattices of varieties
Keywords:
subvarieties
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References:
[1] Sheiia Oates MacDonald andM. R. Vaughan-Lee,Varieties that make one Cross. J. Austral. Math. Soc. Ser. A26 (1978), 368-382. · Zbl 0393.17001
[2] V. L. Murskii,The existence in three-valued logic of a closed class with finite basis not having a finite complete system of identities. Soviet Math. Doklady6 (1965), 1020-1024. · Zbl 0154.25506
[3] Sheila Oates-Williams,Murskii’s algebra does not satisfy MIN. Bull. Austral. Math. Soc.22 (1980), 199-203. · Zbl 0487.08008
[4] Caroline Ruth Shallon,Non-finitely based binary algebras derived from lattices. Ph.D. thesis, University of California, Los Angeles, 1979.
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