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 in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A̲ . In this paper we characterize transitive graph algebras, identities and hyperidentities in transitive graph algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1091,
author = {Tiang Poomsa-ard and Jeerayut Wetweerapong and Charuchai Samartkoon},
title = {Hyperidentities in transitive graph algebras},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {25},
year = {2005},
pages = {23-37},
zbl = {1102.08004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1091}
}
Tiang Poomsa-ard; Jeerayut Wetweerapong; Charuchai Samartkoon. Hyperidentities in transitive graph algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 25 (2005) pp. 23-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1091/
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