ИСТИНА

We recall the notion of an essential relation, a key relation, and the pattern of a key relation. Note that every critical relation is a key relation, and therefore, any relational clone can be generated by only key relations from it. We say that a relation ρ has full pattern if for every i, j and ai, bi we have (a1, ..., an), (a1, ..., aj-1, bj, aj+1, ..., an), (a1, ..., ai-1, bi, ai+1, ..., an) ∈ ρ⇒(a1, ..., ai-1, bi, ai+1, ..., aj-1, bj, aj+1, ..., an) ∈ ρ. We prove that every key relation with full pattern preserved by a weak near-unanimity operation is a union of blocks, where each block can be defined by a linear equation.