Pairwise comaximal elements and the classification of all ∨-distributive triangular norms of length 3

For a lattice with a ∨-distributive t-norm, one useful inequality is obtained. Theorems on relations between a family of pairwise comaximal elements and a direct decomposition of the unit in a lattice with a ∨-distributive t-norm have given. Using these results, the description of all ∨-distributive triangular norms of length 3 and all lattices of length 3 with a ∨-distributive t-norm have obtained.