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Subvarieties of BL-algebras generated by single-component chains

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Abstract.

 In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains, called ŁΠG.

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Authors and Affiliations

  1. Università di Salerno, Dipartamento di Matematica e informatica, Fac. di Scienze, via S. Allende, 84081 Baronisi, Salerno, Italy. e-mail: dinola@cds.unina.it, , , , , , IT

    Antonio Di Nola

  2. Institut d'Investigació en Intel$\cdot$ligència Artificial (IIIA), Consejo Superior de Investigaciones Cientí´ficas (CSIC), Campus Universitat Autònoma de Barcelona, s/n, 08193 Bellaterra, Spain. e-mail: {esteva;godo;garcia}@iiia.csic.es, , , , , , ES

    Francesc Esteva, Pere Garcia & Lluís Godo

  3. Istituto di Matematica, Facoltà di Architettura, Università di Napoli, Via Monteliveto 3, 80134 Napoli, Italy. e-mail: sessa@cds.unina.it, , , , , , IT

    Salvatore Sessa

Authors
  1. Antonio Di Nola
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  2. Francesc Esteva
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  3. Pere Garcia
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  4. Lluís Godo
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  5. Salvatore Sessa
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Received: 8 January 2001 / Published online: 12 July 2002

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Di Nola, A., Esteva, F., Garcia, P. et al. Subvarieties of BL-algebras generated by single-component chains. Arch. Math. Logic 41, 673–685 (2002). https://doi.org/10.1007/s001530100114

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  • DOI: https://doi.org/10.1007/s001530100114

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