Geodesic
Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 81-107.

Voir la notice de l'article provenant de la source Library of Science

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 a term equation s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. A class of graph algebras V is called a graph variety if V = Mod_g Σ where Σ is a subset of T(X) × T(X). A graph variety V' = Mod_gΣ' is called a biregular leftmost graph variety if Σ' is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety V if A(G) satisfies s ≈ t for all G ∈ V. An identity s ≈ t of a variety V is called a hyperidentity of a graph algebra A(G), G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations of A(G) of the appropriate arity, the resulting identities hold in A(G). An identity s ≈ t of a variety V is called an M-hyperidentity of a graph algebra A(G), G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations in a subgroupoid M of term operations of A(G) of the appropriate arity, the resulting identities hold in A(G).
Keywords: varieties, biregular leftmost graph varieties, identities, term, hyperidentity, M-hyperidentity, binary algebra, graph algebra 
@article{DMGAA_2009_29_2_a0,
     author = {Anantpinitwatna, Apinant and Poomsa-ard, Tiang},
     title = {Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {81--107},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a0/}
}
TY  - JOUR
AU  - Anantpinitwatna, Apinant
AU  - Poomsa-ard, Tiang
TI  - Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2009
SP  - 81
EP  - 107
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a0/
LA  - en
ID  - DMGAA_2009_29_2_a0
ER  - 
%0 Journal Article
%A Anantpinitwatna, Apinant
%A Poomsa-ard, Tiang
%T Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)
%J Discussiones Mathematicae. General Algebra and Applications
%D 2009
%P 81-107
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a0/
%G en
%F DMGAA_2009_29_2_a0
Anantpinitwatna, Apinant; Poomsa-ard, Tiang. Special m-hyperidentities in biregular leftmost graph varieties of type (2,0). Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 81-107. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a0/

[1] A. Ananpinitwatna and T. Poomsa-ard, Identities in biregular leftmost graph varieties of type (2,0), Asian-European J. of Math. 2 (1) (2009), 1-18.

[2] A. Ananpinitwatna and T. Poomsa-ard, Hyperidentities in biregular leftmost graph varieties of type (2,0), Int. Math. Forum 4 (18) (2009), 845-864.

[3] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, Chapman and Hall/CRC 2002.

[4] K. Denecke and T. Poomsa-ard, Hyperidentities in graph algebras, Contributions to General Algebra and Aplications in Discrete Mathematics, Potsdam (1997), 59-68.

[5] K. Denecke, D. Lau, R. Pöschel and D. Schweigert, Hyperidentities, hyperequational classes and clone congruences, Verlag Hölder-Pichler-Tempsky, Wien, Contributions to General Algebra 7 (1991), 97-118.

[6] M. Krapeedang and T. Poomsa-ard, Biregular leftmost graph varieties of type (2,0), accepted to publish in AAMS.

[7] E.W. Kiss, R. Pöschel and P. Pröhle, Subvarieties of varieties generated by graph algebras, Acta Sci. Math. 54 (1990), 57-75.

[8] J.Khampakdee and T. Poomsa-ard, Hyperidentities in (xy)x ≈ x(yy) graph algebras of type (2,0), Bull. Khorean Math. Soc. 44 (4) (2007), 651-661.

[9] J. Płonka, Hyperidentities in some of vareties, pp. 195-213 in: General Algebra and discrete Mathematics ed. by K. Denecke and O. Lüders, Lemgo 1995.

[10] J. Płonka, Proper and inner hypersubstitutions of varieties, pp. 106-115 in: 'Proceedings of the International Conference: Summer School on General Algebra and Ordered Sets 1994', Palacký University Olomouce 1994.

[11] T. Poomsa-ard, Hyperidentities in associative graph algebras, Discussiones Mathematicae General Algebra and Applications 20 (2) (2000), 169-182.

[12] T. Poomsa-ard, J. Wetweerapong and C. Samartkoon, Hyperidentities in idempotent graph algebras, Thai Journal of Mathematics 2 (2004), 171-181.

[13] T. Poomsa-ard, J. Wetweerapong and C. Samartkoon, Hyperidentities in transitive graph algebras, Discussiones Mathematicae General Algebra and Applications 25 (1) (2005), 23-37.

[14] R. Pöschel, The equational logic for graph algebras, Zeitschr.f.math. Logik und Grundlagen d. Math. Bd. S. 35 (1989), 273-282.

[15] R. Pöschel, Graph algebras and graph varieties, Algebra Universalis 27 (1990), 559-577.

[16] R. Pöschel and W. Wessel, Classes of graph definable by graph algebras identities or quasiidentities, Comment. Math. Univ, Carolinae 28 (1987), 581-592.

[17] C.R. Shallon, Nonfinitely based finite algebras derived from lattices, Ph. D. Dissertation, Uni. of California, Los Angeles 1979.