Hyperidentities in $(xx)y \approx x(yx)$ Graph Algebras of Type (2; 0)

W. Hemvong, T. Poomsa-ard

Abstract

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). A graph G satisfies an identity $s \approx t$ if the corresponding graph algebra A(G) satisfies $s \approx t$. G is called a $(xx)y \approx x(yx)$ graph if A(G) satisfies the equation $(xx)y \approx x(yx)$. An identity $s \approx t$ of terms s and t of any type $\tau$ is called a hyperidentity of an algebra $\underline{A}$ if whenever the operation symbols occurring in s and t are replaced by any term operations of $\underline{A}$ of the appropriate arity, the resulting identities hold in $\underline{A}$.In this paper we characterize $(xx)y \approx x(yx)$ graph algebras, identities and hyperidentities in $(xx)y \approx x(yx)$ graph algebras.