The Lattice of Filters of a Pseudo BL-Algebra

Jeflea Antoneta ()
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Jeflea Antoneta: “Spiru Haret” University of Constanta

Ovidius University Annals, Economic Sciences Series, 2011, vol. XI, issue 1, 1086-1089

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.

Keywords: filters; pseudo BL-algebra; normal filters; maximal elements (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:ovi:oviste:v:11:y:2011:i:1:p:1086-1089

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