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Murskii's algebra does not satisfy min

Published online by Cambridge University Press:  17 April 2009

Sheila Oates-Williams
Sheila Oates-Williams
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland 4067, Australia.
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Abstract

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This note shows that the variety generated by Murskii's 3-element algebra contains an infinite descending chain of subvarieties, thus falsifying a conjecture made previously by the author and M.R. Vaughan-Lee.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 2 , October 1980 , pp. 199 - 203
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Macdonald, Sheila Oates and Vaughan-Lee, M.R., “Varieties that make one Cross”, J. Austral. Math. Soc. Ser. A 26 (1978), 368–382.CrossRefGoogle Scholar
[2]Murskii˘, V.L., “The existence in three-valued logic of a closed class with finite basis, not having a finite complete system of identities”, Soviet Math. Dokl. 6 (1965), 1020–1024.Google Scholar
[3]Shallon, Caroline Ruth, “Non-finitely based binary algebras derived from lattices” (PhD thesis, University of California, Los Angeles, 1979).Google Scholar