Studia Logica

, Volume 69, Issue 3, pp 329–338

A Generalization of the Łukasiewicz Algebras

  • Teresa Almada
  • JÚlia Vaz de Carvalho

DOI: 10.1023/A:1013846725213

Cite this article as:
Almada, T. & Vaz de Carvalho, J. Studia Logica (2001) 69: 329. doi:10.1023/A:1013846725213


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

Congruence extension propertyPerfect extensionLocally finite varietyEquationally definable principal congruencesSubdirectly irreducible algebraSimple algebra

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Teresa Almada
    • 1
  • JÚlia Vaz de Carvalho
    • 2
  1. 1.Departamento de Matem[aacutUniversidade de LisboaLisboaPortugal
  2. 2.Centro de [AacutUniversidade de LisboaLisboaPortugal