On The Lattice of Filters of A Pseudo-BL Algebra
Dumitru Busneag and Dana Piciu
Fora pseudo -BL algebra A we denote by F(A)(Fn (A)) the lattice of all filters (normal filters) of A. The aim of this paper is to put in evidence new characterisations for the maximal and prime elements on F (A)(Fn (A)).
Also,we obtain some new rules of calculus in pseudo-BL algebras and some results about the sublattice Fn (A) of F (A). We characterize the pseudo-BL algebras for which the lattice of filters (normal filters) is a Boolean lattice.
Archimedean and hyperarchimedean pseudo-BL algebras are characterized.In the end we prove a theorem of Nachbin type for pseudo-BL algebras.
AMS Subject Classification 2000: 03G10, 03G25, 06D35.