Weak coherence of congruences
Ivan Chajda · Czechoslovak Mathematical Journal · 1991
The concept of coherent congruences and algebras comes from D. Geiger [5]: An algebra A is coherent iffor every its subalgebra B and each Ѳ є Con A, if [Ь] ѳ с в for some b є Б, then [x] 0 e Б for each x є Б.In other words, A is coherent if every its subalgebra containing at least one congruence class of some Ѳ є Con A is the union of congruence classes of Ѳ.A variety У is coherent if each A є i^ has this property.D. Geiger [5] proved that Y is coherent if and only if there exist an (n + l)-ary term h and ternary terms t h i = 1,..., n such that ft(x, ii(x, y, z), ..., f"(x, y, z)) = y and ri(x, x, z) = z for i = 1, ..., n .