ABSTRACT. Pseudo-BL-algebras are a noncommutative extention of BL-algebras. In this paper we consider polars in pseudo-BL-algebras and the class of complete pseudo-BL-algebras. In the final section, a version of the CantorBernstein theorem will be proved.

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Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF-filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of IF-filters and direct product of IF-filters are studied.