Title | The variety generated by perfect BL-algebras: an algebraic approach in a fuzzy setting |

Publication Type | Journal Article |

Year of Publication | 2002 |

Authors | Di Nola A [1], Sessa S [2], Esteva F [3], Godo L [4], García P [5] |

Journal | Annals of Mathematics and Artificial Intelligence |

Volume | 35 |

Number | 1-4 |

Pagination | 197-214 |

Abstract | BL-algebras are the Lindembaum algebras of the propositional calculus coming from the continuous triangular norms and their residua in the real unit interval. Any BL-algebra is a subdirect product of local (linear)BL-algebras. A local BL-algebra is either locally finite (and hence an MV-algebra) or perfect or peculiar. Here we study extensively perfect BL-algebras characterizing, with a finite scheme of equations, the generated variety. We first establish some results for general BL-algebras, afterwards the variety is studied in detail. All the results are parallel to those ones already existing in the theory of perfect MV-algebras, but these results must be reformulated and reproved in a different way, because the axioms of BL-algebras are obviously weaker than those for MV-algebras. |