The Blok-Ferreirim theorem for normal GBL-algebras and its application

• Autores: Peter Jipsen, F. Montagna
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 60, Nº. 4, 2009, págs. 381-404
• Idioma: inglés
• DOI: 10.1007/s00012-009-2106-4
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• Resumen

  • Generalized basic logic algebras (GBL-algebras for short) have been introduced in [JT02] as a generalization of Hájek�s BL-algebras, and constitute a bridge between algebraic logic and l-groups. In this paper we investigate normal GBL-algebras, that is, integral GBL-algebras in which every filter is normal. For these structures we prove an analogue of Blok and Ferreirim�s [BF00] ordinal sum decomposition theorem. This result allows us to derive many interesting consequences, such as the decidability of the universal theory of commutative GBL-algebras, the fact that n-potent GBL-algebras are commutative, and a representation theorem for finite GBL-algebras as poset sums of GMV-algebras, a result which generalizes Di Nola and Lettieri�s [DL03] representation of finite BL-algebras.