The distributive equations for idempotent uninorms and nullnorms

The distributive equations only involving idempotent uninorms and nullnorms are investigated. The following two cases are proved: (i) As for a nullnorm with an idempotent uninorm having distributivity, the necessary and sufficient conditions are given. (ii) As for an idempotent uninorm with a nullnorm having distributivity, the necessary and sufficient conditions are given also.