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Free Algebras in Varieties of Glivenko MTL-algebras Satisfying the Equation 2(x2) = (2x)2

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An Erratum to this article was published on 30 June 2016

Abstract

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras.

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Authors and Affiliations

  1. Instituto Argentino de Matem´tica, CONICET, Saavedra 15, Piso 3, 1083, Buenos Aires, ARGENTINA

    Roberto Cignoli

  2. Facultat de Matem´tiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, SPAIN

    Antoni Torrens Torrell

Authors
  1. Roberto Cignoli
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  2. Antoni Torrens Torrell
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Correspondence to Roberto Cignoli.

Additional information

Dedicated to the memory of Willem Johannes Blok

2000 Mathematics Subject Classification: 06D72, 06E15, 08B20.

The second author was partially supported by grants MTM2004-03101 and TIN2004-07933-C03-02 of M.E.C. of Spain

Dedicated to the memory of Willem Johannes Blok

An erratum to this article is available at http://dx.doi.org/10.1007/s11225-016-9678-8.

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Cignoli, R., Torrell, A.T. Free Algebras in Varieties of Glivenko MTL-algebras Satisfying the Equation 2(x2) = (2x)2. Stud Logica 83, 157–181 (2006). https://doi.org/10.1007/s11225-006-8302-8

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  • DOI: https://doi.org/10.1007/s11225-006-8302-8

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