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Decomposability of free Łukasiewicz implication algebras

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Abstract

Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be only decomposed into a direct product of two factors, one of which is the two-element implication algebra.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Nacional del Sur, Avenida Alem 1253, 8000, Bahía Blanca, Argentina

    Jose Patricio Díaz Varela

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Antoni Torrens Torrell

Authors
  1. Jose Patricio Díaz Varela
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  2. Antoni Torrens Torrell
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Correspondence to Jose Patricio Díaz Varela.

Additional information

This paper was prepared while the first author was visiting the University of Barcelona, partially supported by Universidad Nacional del Sur, CONICET and Fundación Carolina. The second author was partially supported by grants MTM2004-03101 and TIN2004-07933-C03-02 of M.E.C. of España.

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Díaz Varela, J.P., Torrens Torrell, A. Decomposability of free Łukasiewicz implication algebras. Arch. Math. Logic 45, 1011–1020 (2006). https://doi.org/10.1007/s00153-006-0023-1

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  • DOI: https://doi.org/10.1007/s00153-006-0023-1

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