Dumitru Busnea 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 paperis 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.