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Hyperidentities in associative graph algebras

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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.
Twórcy
  • Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Bibliografia
  • [1] K. Denecke and M. Reichel, Monoids of Hypersubstitutions and M-solidvarieties, Contributions to General Algebra 9 (1995), 117-125.
  • [2] K. Denecke and T. Poomsa-ard, Hyperidentities in graph algebras, 'General Algebra and Aplications in Discrete Mathematics', Shaker-Verlag, Aachen 1997, 59-68.
  • [3] E.W. Kiss, R. Pöschel, and P. Pröhle, Subvarieties of varieties generated by graph algebras, Acta Sci. Math. (Szeged) 54 (1990), 57-75.
  • [4] J. Płonka, Hyperidentities in some classes of algebras, preprint, 1993.
  • [5] J. Płonka, Proper and inner hypersubstitutions of varieties, 'General Algebra nd Ordered Sets', Palacký Univ., Olomouc 1994, 106-116.
  • [6] R. Pöschel, The equatioal logic for graph algebras, Zeitschr. Math. Logik Grundlag. Math. 35 (1989), 273-282.
  • [7] R. Pöschel, Graph algebras and graph varieties, Algebra Universalis 27 (1990), 559-577.
  • [8] C.R. Shallon, Nonfinitely based finite algebras derived from lattices, Ph. D. Disertation, Univ. of California, Los Angeles 1979.
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1014
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