Abstract

In this paper we pursue the study of the variety $ L_n ^ m $ of m - generalized? ukasiewicz algebras of order n which was initiated in [ 1 ]. This variety contains the variety of? ukasiewicz algebras of order n. Given A? $ \ in L_n ^ m $, we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain? ukasiewicz 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 $ L_n ^ m $. After showing that for m > 1 and n > 2, the variety of? ukasiewicz algebras of order n is a proper subvariety of $ L_n ^ m $, we prove that $ L_n ^ m $ is a finitely generated discriminator variety and point out some consequences of this strong property, one of which is congruence permutability.