Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-26T18:10:29.449Z Has data issue: false hasContentIssue false
  • English
  • Français

Cyclic Tarski algebras

Published online by Cambridge University Press:  17 April 2009

Marta A. Zander
Marta A. Zander
Affiliation:
Departamento de Matemática, Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina, e-mail: mzander@criba.edu.ar
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The variety of cyclic Boolean algebras is a particular subvariety of the variety of tense algebras. The objective of this paper is to study the variety  of {→,g, h}-subreducts of cyclic Boolean algebras, which we call cyclic Tarski algebras. We prove that  is generated by its finite members and we characterise the locally finite subvarieties of . We prove that there are no splitting varieties in the lattice Λ() of subvarieties of . Finally, we prove that the subquasivarieties and the subvarieties of a locally finite subvariety of  coincide.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 147 - 158
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Abad, M. and Díaz Varela, J.P., ‘Representation of cubic lattices by symmetric implication algebras’ (to appear).Google Scholar
[2]Abad, M., Díaz Varela, J.P. and Zander, M., ‘Boolean algebras with a distinguished automorphism’, Rep. Math. Logic 37 (2003), 101–112.Google Scholar
[3]Abad, M., Díaz Varela, J.P. and Zander, M., ‘Varieties and quasivarieties of monadic Tarski algebras’, Sci. Math. Jpn. 56 (2002), 599–612.Google Scholar
[4]Abbott, J.C., ‘Semi-boolean algebras’, Mat. Vesnik 19 (1967), 177–198.Google Scholar
[5]Abbott, J.C., ‘Implicational algebras’, Bull. Math. Soc. Sci. Math R. S. Roumaine 11 (1967), 3–23.Google Scholar
[6]Bezhanishvili, G., ‘Locally finite varieties’, Algebra Universalis 46 (2001), 531–548.CrossRefGoogle Scholar
[7]Gispert, J. and Torrens, A., ‘Locally finite quasivarieties of MV-algebras’, (preprint).Google Scholar
[8]Kowalski, T., ‘Varieties of tense algebras’, Rep. Math. Logic 32 (1998), 53–95.Google Scholar
[9]McKenzie, R., ‘Equational bases and nonmodular lattice varieties’, Trans. Amer. Math. Soc. 174 (1972), 1–43.CrossRefGoogle Scholar