TY - JOUR

T1 - On the Variety of m-generalized Lukasiewicz Algebras of Order n

AU - Carvalho, Júlia Maria Nunes Loureiro Vaz de

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this paper we pursue the study of the variety L-n(m) of m-generalized Lukasiewicz algebras of order n which was initiated in [1]. This variety contains the variety of Lukasiewicz algebras of order n. Given A is an element of L-n(m), we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Lukasiewicz 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 Lukasiewicz 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.

AB - In this paper we pursue the study of the variety L-n(m) of m-generalized Lukasiewicz algebras of order n which was initiated in [1]. This variety contains the variety of Lukasiewicz algebras of order n. Given A is an element of L-n(m), we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Lukasiewicz 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 Lukasiewicz 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.

KW - m-generalized Lukasiewicz algebra of order n

KW - congruence permutable variety

KW - congruence regular variety

KW - congruence uniform variety

KW - finitely generated variety

KW - Lukasiewicz algebra of order n

KW - equationally definable principal congruences

KW - filtral variety

KW - congruence coherent variety

KW - discriminator variety

U2 - 10.1007/s11225-010-9236-8

DO - 10.1007/s11225-010-9236-8

M3 - Article

VL - 94

SP - 291

EP - 305

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 2

ER -