The subdirectly irreducible algebras in the variety generated by graph algebras

• Autores: Marcin Kozik, Gábor Kun
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 58, Nº. 2, 2008, págs. 229-242
• Idioma: inglés
• DOI: 10.1007/s00012-008-2053-5
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• Resumen

  • 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.