PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Discussiones Mathematicae - General Algebra and Applications

2000 | 20 | 2 | 169-182
Tytuł artykułu

### Hyperidentities in associative 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 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.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
169-182
Opis fizyczny
Daty
wydano
2000
otrzymano
1997-06-29
poprawiono
1999-04-15
poprawiono
1999-11-30
Twórcy
autor
• 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.
Typ dokumentu
Bibliografia
Identyfikatory