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 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 A. In this paper we characterize associative graph algebras, identities in associative graph algebras and hyperidentities in associative graph algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1014,
author = {Tiang Poomsa-ard},
title = {Hyperidentities in associative graph algebras},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {20},
year = {2000},
pages = {169-182},
zbl = {0977.08006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1014}
}
Tiang Poomsa-ard. Hyperidentities in associative graph algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 20 (2000) pp. 169-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1014/
[000] [1] K. Denecke and M. Reichel, Monoids of Hypersubstitutions and M-solidvarieties, Contributions to General Algebra 9 (1995), 117-125. | Zbl 0884.08008
[001] [2] K. Denecke and T. Poomsa-ard, Hyperidentities in graph algebras, 'General Algebra and Aplications in Discrete Mathematics', Shaker-Verlag, Aachen 1997, 59-68. | Zbl 0915.08004
[002] [3] E.W. Kiss, R. Pöschel, and P. Pröhle, Subvarieties of varieties generated by graph algebras, Acta Sci. Math. (Szeged) 54 (1990), 57-75. | Zbl 0713.08006
[003] [4] J. Płonka, Hyperidentities in some classes of algebras, preprint, 1993.
[004] [5] J. Płonka, Proper and inner hypersubstitutions of varieties, 'General Algebra nd Ordered Sets', Palacký Univ., Olomouc 1994, 106-116.
[005] [6] R. Pöschel, The equatioal logic for graph algebras, Zeitschr. Math. Logik Grundlag. Math. 35 (1989), 273-282. | Zbl 0661.03020
[006] [7] R. Pöschel, Graph algebras and graph varieties, Algebra Universalis 27 (1990), 559-577. | Zbl 0725.08002
[007] [8] C.R. Shallon, Nonfinitely based finite algebras derived from lattices, Ph. D. Disertation, Univ. of California, Los Angeles 1979.