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Discussiones Mathematicae General Algebra and Applications 20(2) (2000) 169-182
DOI: https://doi.org/10.7151/dmgaa.1014

HYPERIDENTITIES IN ASSOCIATIVE GRAPH ALGEBRAS

Tiang Poomsa-ard

Department of Mathematics, Faculty of Science,
Khon Kaen University, Khon Kaen 40002, Thailand
e-mail: tiang@kku1.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 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 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 associative graph algebras, identities in associative graph algebras and hyperidentities in associative graph algebras.

Keywords: identities, hyperidentities, associative graph algebras, terms.

1991 Mathematics Subject Classifications: 08B05, 0840, 08C10, 08C99, 03C05.

References

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Received 29 June 1997
Revised 15 April 1999
Revised 30 November 1999