∨-distributive n-ary semicopulas on lattices

In the present paper, definitions of an n-ary semicopula on a bounded lattice L, a ∨-distributive n-ary semicopula on L and an infinite ∨-distributive n-ary semicopula on L are introduced. A relation between the set of all bounded lattices L with a ∨-distributive n-ary semicopula on L and the set of all bounded lattices L with a ∨-distributive m-ary semicopula on L  , where 2≤n,2≤m,n≠m2≤n,2≤m,n≠m, is obtained. The method is given for investigation of the following questions: a description of all bounded lattices L such that every n-ary semicopula on L is ∨-distributive and a description of all complete lattices L such that every n-ary semicopula on L is infinite ∨-distributive.