\ of monadic m-generalized Łukasiewicz algebras of order n -algebras), namely a generalization of monadic n-valued Łukasiewicz algebras. In this article, we determine the congruences and we characterized the subdirectly irreducible \-algebras. From this last result we proved that \ is a discriminator variety and as a consequence we characterized the principal congruences. In the last part of this paper we find an immersion of these algebras in a functional algebra and we proved that in the finite case they are (...) isomorphic. This last result allows to show a new functional representation for monadic n-valued Łukasiewicz algebras. Finally, we define the notions of \-algebra of fractions and maximal algebra of fractions and we prove the existence of a maximal \-algebra of fractions for an \-algebra. (shrink)

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. (shrink)