Generalized basic logic algebras (GBL-algebras for short) have been introduced in [JT02] as a generalization of Hajek'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.

Jipsen, P., Montagna, F. (2009). The Blok-Ferreirim theorem for normal GBL algebras and application. ALGEBRA UNIVERSALIS, 60(4), 381-404 [10.1007/s00012-009-2106-4].

The Blok-Ferreirim theorem for normal GBL algebras and application

MONTAGNA, FRANCO
2009-01-01

Abstract

Generalized basic logic algebras (GBL-algebras for short) have been introduced in [JT02] as a generalization of Hajek'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.
2009
Jipsen, P., Montagna, F. (2009). The Blok-Ferreirim theorem for normal GBL algebras and application. ALGEBRA UNIVERSALIS, 60(4), 381-404 [10.1007/s00012-009-2106-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/17498
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