The subdirectly irreducible algebras in the variety generated by graph algebras

. We show that every non-trivial subdirectly irreducible algebra in the variety generated by graph algebras is either a two-element left zero semigroup or a graph algebra itself. We characterize all the subdirectly irreducible algebras in this variety. From this we derive an example of a groupoid (g...

Full description

Saved in:
Bibliographic Details
Published inAlgebra universalis Vol. 58; no. 2; pp. 229 - 242
Main Authors Kozik, Marcin, Kun, Gábor
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.03.2008
Subjects
Algebra
Mathematics
Mathematics and Statistics
08B26
the variety membership problem
68Q17
graph algebras
computational complexity
groupoids
Online AccessGet full text
ISSN0002-5240
1420-8911
DOI10.1007/s00012-008-2053-5

Cover

More Information
Summary:. We show that every non-trivial subdirectly irreducible algebra in the variety generated by graph algebras is either a two-element left zero semigroup or a graph algebra itself. We characterize all the subdirectly irreducible algebras in this variety. From this we derive an example of a groupoid (graph algebra) that generates a variety with NP-complete membership problem. This is an improvement over the result of Z. Székely who constructed an algebra with similar properties in the signature of two binary operations.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-008-2053-5