Abstract.
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.
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Received April 3, 2006; accepted in final form February 8, 2007.
The second author was supported by OTKA grants no. T043671, NK67867, K67870 and by NKTH (National Office for Research and Technology, Hungary).
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Kozik, M., Kun, G. The subdirectly irreducible algebras in the variety generated by graph algebras. Algebra univers. 58, 229–242 (2008). https://doi.org/10.1007/s00012-008-2053-5
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DOI: https://doi.org/10.1007/s00012-008-2053-5