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The Lattice of Filters of a Pseudo BL-Algebra

Author

Listed:
  • Jeflea Antoneta

    (“Spiru Haret” University of Constanta)

Abstract

In this paper we begin the investigation of filters and congruences. We define the filters of a pseudo BL-algebra A and we denote by F(A) ()(AFn) lattice of all filters (normal filters) of A; we put in evidence some results about these lattices. By using the two distance functions we define two binary relations )(FL=and )(FR=, related to a filter F of A; these two relations are equivalence relations, but they are not congruences. They quotient set )(/FLAand )(/FRAare bounded distributive lattices. We give characterizations for the maximal and prime elements on F(A) ()(AFn) and we prove the prime filter theorem. We characterize the pseudo BL-algebras for which the lattice of filters (normal filters) is a Boolean lattice and the archimedean and hyperarchimedean pseudo BL-algebras.

Suggested Citation

  • Jeflea Antoneta, 2011. "The Lattice of Filters of a Pseudo BL-Algebra," Ovidius University Annals, Economic Sciences Series, Ovidius University of Constantza, Faculty of Economic Sciences, vol. 0(1), pages 1086-1089, May.
    • Handle: RePEc:ovi:oviste:v:11:y:2011:i:1:p:1086-1089
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    More about this item

    Keywords

    filters; pseudo BL-algebra; normal filters; maximal elements;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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