Hyperidentities in associative graph algebras

Tiang Poomsa-ard

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 2, page 169-182
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Tiang Poomsa-ard. "Hyperidentities in associative graph algebras." Discussiones Mathematicae - General Algebra and Applications 20.2 (2000): 169-182. <http://eudml.org/doc/287737>.

@article{TiangPoomsa2000,
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 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.},
author = {Tiang Poomsa-ard},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {identities; hyperidentities; associative graph algebras; terms; varieties of associative graph algebras},
language = {eng},
number = {2},
pages = {169-182},
title = {Hyperidentities in associative graph algebras},
url = {http://eudml.org/doc/287737},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Tiang Poomsa-ard
TI - Hyperidentities in associative graph algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 2
SP - 169
EP - 182
AB - 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.
LA - eng
KW - identities; hyperidentities; associative graph algebras; terms; varieties of associative graph algebras
UR - http://eudml.org/doc/287737
ER -

References

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  1. [1] K. Denecke and M. Reichel, Monoids of Hypersubstitutions and M-solidvarieties, Contributions to General Algebra 9 (1995), 117-125. Zbl0884.08008
  2. [2] K. Denecke and T. Poomsa-ard, Hyperidentities in graph algebras, 'General Algebra and Aplications in Discrete Mathematics', Shaker-Verlag, Aachen 1997, 59-68. Zbl0915.08004
  3. [3] E.W. Kiss, R. Pöschel, and P. Pröhle, Subvarieties of varieties generated by graph algebras, Acta Sci. Math. (Szeged) 54 (1990), 57-75. Zbl0713.08006
  4. [4] J. Płonka, Hyperidentities in some classes of algebras, preprint, 1993. 
  5. [5] J. Płonka, Proper and inner hypersubstitutions of varieties, 'General Algebra nd Ordered Sets', Palacký Univ., Olomouc 1994, 106-116. 
  6. [6] R. Pöschel, The equatioal logic for graph algebras, Zeitschr. Math. Logik Grundlag. Math. 35 (1989), 273-282. Zbl0661.03020
  7. [7] R. Pöschel, Graph algebras and graph varieties, Algebra Universalis 27 (1990), 559-577. Zbl0725.08002
  8. [8] C.R. Shallon, Nonfinitely based finite algebras derived from lattices, Ph. D. Disertation, Univ. of California, Los Angeles 1979. 

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