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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 correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(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...
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 a term equation s ≈ t if the corresponding graph algebra satisfies s ≈ t. A class of graph algebras V is called a graph variety if where Σ is a subset of T(X) × T(X). A graph variety is called a biregular leftmost graph variety if Σ’ is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety...
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 transitive graph if the corresponding graph algebra A(G) satisfies the equation x(yz) ≈ (xz)(yz). An identity s ≈ t of terms s and t of any type t is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring...
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