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Discussiones Mathematicae General Algebra and Applications 25(1) (2005) 23-37
DOI: https://doi.org/10.7151/dmgaa.1091

HYPERIDENTITIES IN TRANSITIVE GRAPH ALGEBRAS

Tiang Poomsa-ard, Jeerayut Wetweerapong and Charuchai Samartkoon

Department of Mathematics, Faculty of Science,
Khon Kaen University,
Khon Kaen 40002, Thailand
e-mails: tiang@kku.ac.th, wjeera@kku.ac.th

Abstract

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 A 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 A.

In this paper we characterize transitive graph algebras, identities and hyperidentities in transitive graph algebras.

Keywords: identity, hyperidentity, term, normal form term, binary algebra, graph algebra, transitive graph algebra.

2000 Mathematics Subject Classification: 08B05, 08B99, 08C99, 03C05, 05C99.

References

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Received 30 December 2004
Revised 3 March 2005