Abstract.
We generalize Komori’s characterization of the proper subvarieties of MV-algebras. Namely, within the variety of generalized MV-algebras (GMV-algebras) such that every maximal ideal is normal, we characterize the proper top varieties. In addition, we present equational bases for these top varieties. We show that there are only countably many different proper top varieties and each of them has uncountably many subvarieties. Finally, we study coproducts and we show that the amalgamation property fails for the class of n-perfect GMV-algebras, i.e., GMV-algebras that can be split into n + 1 comparable slices.
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Received December 4, 2006; accepted in final form July 31, 2007.
This paper has been supported by the Center of Excellence SAS -Physics of Information-I/2/2005, the grant VEGA No. 2/6088/26 SAV, by Science and Technology Assistance Agency under the contracts No. APVT-51-032002, APVV-0071-06, Bratislava.
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Dvurečenskij, A., Holland, W.C. Komori’s characterization and top varieties of GMV-algebras. Algebra univers. 60, 37–62 (2009). https://doi.org/10.1007/s00012-008-2085-x
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DOI: https://doi.org/10.1007/s00012-008-2085-x