HYPERIDENTITIES IN (xy)x ≈x(yy) GRAPH ALGEBRAS OF TYPE (2,0)

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 44, Issue 4, 2007, pp.651-661
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2007.44.4.651

Title & Authors

HYPERIDENTITIES IN (xy)x ≈x(yy) GRAPH ALGEBRAS OF TYPE (2,0)

Khampakdee, Jeeranunt; Poomsa-Ard, Tiang;

Khampakdee, Jeeranunt; Poomsa-Ard, Tiang;

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 if the corresponding graph algebra satisfies . A graph G=(V,E) is called an graph if the graph algebra satisfies the equation . An identity of terms s and t of any type is called a hyperidentity of an algebra if whenever the operation symbols occurring in s and t are replaced by any term operations of of the appropriate arity, the resulting identities hold in . In this paper we characterize graph algebras, identities and hyperidentities in graph algebras.

Keywords

identities;hyperidentities;term;normal form term;binary algebra;graph algebra; graph algebra;

Language

English

Cited by

References

1.

K. Denecke and T. Poomsa-ard, Hyperidentities in graph algebras, Contributions to General Algebra and Applications in Discrete Mathematics, Potsdam 1997, 59-68

2.

K. Denecke and M. Reichel, Monoids of hypersubstitutions and M-solid varieties, Con-tributions to general algebra, 9 (Linz, 1994), 117-126, Holder-Pichler-Tempsky, Vienna, 1995

3.

E. W. Kiss, R. Poschel, and P. Prohle, Subvarieties of varieties generated by graph algebras, Acta Sci. Math. (Szeged) 54 (1990), no. 1-2, 57-75

4.

J. Plonka, Hyperidentities in some of vareties, in: General Algebra and discrete Math- ematics ed. by K. Denecke and O. Luders, Lemgo 1995, 195-213

5.

J. Plonka, Proper and inner hypersubstitutions of varieties, in: Proceedings of the Interna- tional Conference: Summer School on General Algebra and Ordered Sets 1994, Palacky University Olomouce 1994, 106-115

6.

T. Poomsa-ard, Hyperidentities in associative graph algebras, Discuss. Math. Gen. Al-gebra Appl. 20 (2000), no. 2, 169-182

7.

T. Poomsa-ard, J. Wetweerapong, and C. Samartkoon Hyperidentities in Idempotent Graph Algebras, Thai J. Math. 2 (2004), no. 1, 173-182

8.

T. Poomsa-ard, J. Wetweerapong, and C. Samartkoon, Hyperidentities in transitive graph algebras, Discuss. Math. Gen. Algebra Appl. 25 (2005), no. 1, 23-37

9.

R. Poschel, The equational logic for graph algebras, Z. Math. Logik Grundlag. Math. 35 (1989), no. 3, 273-282

11.

C. R. Shallon, Nonfinitely based finite algebras derived from lattices, Ph. D. Dissertation, Uni. of California, Los Angeles, 1979