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