zbMATH — the first resource for mathematics

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.

08B15 Lattices of varieties
Full Text: DOI
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.