Komori's characterization and top varieties of GMV-algebras

• Autores: Anatolij Dvurecenskij, W. Charles Holland
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 60, Nº. 1, 2009, págs. 37-62
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.