### A non commutative generalization of $\u2606$-autonomous lattices

Pseudo $\u2606$-autonomous lattices are non-commutative generalizations of $\u2606$-autonomous lattices. It is proved that the class of pseudo $\u2606$-autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo $\u2606$-autonomous lattices can be described as their normal ideals.