On the variety of M -generalized łukasiewicz algebras of order N

Studia Logica 94 (2):291-305 (2010)
Abstract
In this paper we pursue the study of the variety of m -generalized Łukasiewicz algebras of order n which was initiated in [1]. This variety contains the variety of Łukasiewicz algebras of order n . Given , we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Łukasiewicz algebra of order n and for each congruence on A we find a description via the corresponding Stone filter. We characterize the principal congruences on A via Stone filters. In doing so, we obtain a polynomial equation which defines the principal congruences on the algebras of . After showing that for m > 1 and n > 2, the variety of Łukasiewicz algebras of order n is a proper subvariety of , we prove that is a finitely generated discriminator variety and point out some consequences of this strong property, one of which is congruence permutability.
Keywords Łukasiewicz algebra of order n   m-generalized Łukasiewicz algebra of order n  finitely generated variety  discriminator variety  equationally definable principal congruences  congruence permutable variety  congruence uniform variety  congruence coherent variety  congruence regular variety  filtral variety
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