Hyperidentities in Right Self-distributive Graph Algebras of Type (2,0).

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G)̲ satisfies s ≈ t. A graph G = (V;E) is called a right self-distributive graph if the graph algebra A(G)̲ satisfies the equation ((xy)z) ≈ ((xz)(yz)). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced by any term operations of A̲ of the appropriate arity, the resulting identities hold in A̲. In this paper, we characterize right self-distributive graph algebras, identities and hyperidentities in right self-distributive graph algebras. [ABSTRACT FROM AUTHOR]