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Graph varieties containing Murskii's groupoid

Published online by Cambridge University Press:  17 April 2009

R. Pöschel
Affiliation:
Karl-Weierstrass-Institut für Mathematik, Akademie der Wissenschaften der DDR, Mohrenstr. 39 (Postfach 1304), Berlin, DDR-1086, German Democratic Republic.
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Abstract

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In this paper varieties are investigated which are generated by graph algebras of undirected graphs and—in most cases—contain Murskii's groupoid (that is the graph algebra of the graph with two adjacent vertices and one loop). Though these varieties are inherently nonfinitely based, they can be finitely based as graph varieties (finitely graph based) like, for example, the varitey generated by Murskii's groupoid. Many examples of nonfinitely based graph varities containing Murskii's groupoid are given, too. Moreover, the coatoms in the subvariety lattice of the graph variety of all undirected graphs are described. There are two coatoms and they are finitely graph based.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1989

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