Paper detail

Key (critical) relations preserved by a weak near-unanimity function

In the paper we introduce a notion of a key relation, which is similar to the notion of a critical relation introduced by Keith A.Kearnes and Ágnes Szendrei. All clones on finite sets can be defined by only key relations. In addition there is a nice description of all key relations on 2 elements. These are exactly the relations that can be defined as a disjunction of linear equations. In the paper we show that, in general key relations do not have such a nice description. Nevertheless, we obtain a nice characterization of all key relations preserved by a weak near-unanimity function. This characterization is presented in the paper.