Permutability of Congruences on d\(_{0}\)-Algebras

We introduce a property weaker than congruence-permutability and show that every d \(_{\text {0}}\) ${}_{\text{0}}$ -algebra has this property. We also show that in general d \(_{\text {0}}\) ${}_{\text{0}}$ -algebras are not congruence-permutable, and that a sufficient condition for a d \(_{\text {0}}\) ${}_{\text{0}}$ -algebra to be congruence-permutable is being directed. However this condition is not necessary.