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

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)BLalgebras. A local BL-algebra is either locally finite (and hence an MValgebra) or perfect or peculiar. Here we study extensively perfect BLalgebras 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. Source URL: https://www.iiia.csic.es/en/node/55187 Links [1] https://www.iiia.csic.es/en/staff/antonio-di-nola [2] https://www.iiia.csic.es/en/staff/salvatore-sessa [3] https://www.iiia.csic.es/en/staff/francesc-esteva [4] https://www.iiia.csic.es/en/staff/llu%C3%ADs-godo [5] https://www.iiia.csic.es/en/staff/pere-garc%C3%ADa