Universal varieties of quasi-Stone algebras

Autor: M. E. Adams, Hanamantagouda P. Sankappanavar, Wieslaw Dziobiak
Rok vydání: 2016
Předmět:
Zdroj: Algebra universalis. 76:155-182
ISSN: 1420-8911
0002-5240
DOI: 10.1007/s00012-016-0400-5
Popis: The lattice of varieties of quasi-Stone algebras ordered by inclusion is an $${\omega+1}$$ chain. It is shown that the variety $${\mathbf{Q_{2,2}}}$$ (of height 13) is finite-to-finite universal (in the sense of Hedrlin and Pultr). Further, it is shown that this is sharp; namely, the variety $${\mathbf{Q_{3,1}}}$$ (of height 12) is not finite-to-finite universal and, hence, no proper subvariety of $${\mathbf{Q_{2,2}}}$$ is finite-to-finite universal. In fact, every proper subvariety of $${\mathbf{Q_{2,2}}}$$ fails to be universal. However, $${\mathbf{Q_{1,2}}}$$ (the variety of height 9) is shown to be finite-tofinite universal relative to $${\mathbf{Q_{2,1}}}$$ (the variety of height 8). This too is sharp; namely, no proper subvariety of $${\mathbf{Q_{1,2}}}$$ is finite-to-finite relatively universal. Consequences of these facts are discussed.
Databáze: OpenAIRE
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