Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)

Anantpinitwatna, Apinant ; Poomsa-ard, Tiang

Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 81-107

Résumé

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 A(G) satisfies s ≈ t. A class of graph algebras V is called a graph variety if V = Mod_g Σ where Σ is a subset of T(X) × T(X). A graph variety V' = Mod_gΣ' 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 V if A(G) satisfies s ≈ t for all G ∈ V. An identity s ≈ t of a variety V is called a hyperidentity of a graph algebra A(G), G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations of A(G) of the appropriate arity, the resulting identities hold in A(G). An identity s ≈ t of a variety V is called an M-hyperidentity of a graph algebra A(G), G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations in a subgroupoid M of term operations of A(G) of the appropriate arity, the resulting identities hold in A(G).

Détail

Keywords: varieties, biregular leftmost graph varieties, identities, term, hyperidentity, M-hyperidentity, binary algebra, graph algebra