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AAA76 - 76th Workshop on General Algebra (76. Arbeitstagung Allgemeine Algebra)
May 22-25, 2008
Department of Algebra, Johannes Kepler University Linz
Linz, Austria

Organizers
Erhard Aichinger, Peter Mayr, Matt Nickodemus, Günter Pilz

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HYPERIDENTITIES IN BIREGULAR LEFTMOST GRAPH VARIETIES OF TYPE (2, 0)
by
Prof. Amporn Anantpinitwatna
Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand
Coauthors: Prof. Tiang Poomsa-ard

HYPERIDENTITIES IN BIREGULAR LEFTMOST GRAPH VARIETIES OF TYPE (2, 0)

HYPERIDENTITIES IN BIREGULAR LEFTMOST GRAPH VARIETIES OF TYPE (2, 0)

Amporn Anantpinitwatna and Tiang Poomsa-ard
Department of Mathematics, Faculty of Science,
Mahasarakham University, Mahasarakham 44150, Thailand
E-mail: tiang@kku.ac.th

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 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 = Modg S where S is a subset of T(X)×T(X). A graph variety V' = ModgS' is called a biregular leftmost graph variety if S' is a set of biregular leftmost term equation. 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 a hyperidentity of V if it is a hyperidentities of A(G) for all G ∈ V.

In this paper we characterize all hyperidentities of each biregular leftmost graph varieties in graph algebras.

Date received: March 18, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawc-21.