Bounded residuated lattice ordered monoids (Rl-monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo MV-algebras (or, equivalently, GMV-algebras) and pseudo BL-algebras (and so, particularly, MV-algebras and BL-algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on MV-algebras were studied by Harlenderová and Rachůnek (2006) and on bounded commutative Rl-monoids in our paper which will apear in Math. Slovaca. Now we generalize modal operators to bounded Rl-monoids which need not be commutative and investigate their properties also for further derived algebras.
It is shown that pseudo BL-algebras are categorically equivalent to certain bounded DRl-monoids. Using this result, we obtain some properties of pseudo BL-algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo BL-algebras and, in conclusion, we prove that they form a variety.