, Volume 69, Issue 3, pp 329-338

A Generalization of the Łukasiewicz Algebras

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We introduce the variety ℒ n m , m ≥ 1 and n ≥ 2, of m-generalized Łukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety ℒ n m is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety ℒ n m contains the variety of Łukasiewicz algebras of order n.