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A classification of disjoint unions of two or three copies of the free monogenic semigroup

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Abstract

We prove that, up to isomorphism and anti-isomorphism, there are only two types of semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine types of semigroups which are the union of three copies of the free monogenic semigroup. We provide finite presentations for semigroups of each of these types.

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Acknowledgments

The first author is financially supported by The Ministry of Higher Education in Saudi Arabia (Princess Nora Bint Abdul Rahman University in Riyadh, Ref number RUG0003).

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Correspondence to J. D. Mitchell.

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Communicated by Victoria Gould.

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Abu-Ghazalh, N., Mitchell, J.D., Péresse, Y. et al. A classification of disjoint unions of two or three copies of the free monogenic semigroup. Semigroup Forum 91, 53–61 (2015). https://doi.org/10.1007/s00233-014-9638-4

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  • DOI: https://doi.org/10.1007/s00233-014-9638-4

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