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## Discussiones Mathematicae - General Algebra and Applications

2005 | 25 | 1 | 23-37
Tytuł artykułu

### Hyperidentities in transitive graph algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 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 A̲ .
In this paper we characterize transitive graph algebras, identities and hyperidentities in transitive graph algebras.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
23-37
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-12-30
poprawiono
2005-03-03
Twórcy
autor
• Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
• Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
autor
• Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Bibliografia
• [1] K. Denecke and T. Poomsa-ard, Hyperidentities in graph algebras, 'Contributions to General Algebra and Applications in Discrete Mathematics', Shaker-Verlag, Aachen 1997, 59-68.
• [2] K. Denecke and M. Reichel, Monoids of hypersubstitutions and M-solid varieties, 'Contributions to General Algebra', vol. 9, Verlag Hölder-Pichler-Tempsky, Vienna 1995, 117-125.
• [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 of vareties, 'General Algebra and Discrete Mathematics', Heldermann Verlag, Lemgo 1995, 195-213.
• [5] J. Płonka, Proper and inner hypersubstitutions of varieties, 'Proceedings of the International Conference: 'Summer School on General Algebra and Ordered Sets', Olomouc 1994', Palacký University, Olomouc 1994, 106-115.
• [6] T. Poomsa-ard, Hyperidentities in associative graph algebras, Discuss. Math. - Gen. Algebra Appl. 20 (2000), 169-182.
• [7] R. Pöschel, The equational logic for graph algebras, Z. Math. Logik Grundl. Math. 35 (1989), 273-282.
• [8] R. Pöschel, Graph algebras and graph varieties, Algebra Universalis 27 (1990), 559-577.
• [9] C.R. Shallon, Nonfinitely Based Finite Algebras Derived from Lattices, Ph.D. Thesis, University of California, Los Angeles, CA, 1979.
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Bibliografia
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