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Murskii's algebra does not satisfy min
Published online by Cambridge University Press: 17 April 2009
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
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