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Associate inverse subsemigroups of regular semigroups

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Abstract

By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x∈S, in relation to the natural partial order ≤ S . We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions. As a particular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity element.

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Authors and Affiliations

  1. , Universität Kassel, 34127, Kassel, Germany

    B. Billhardt

  2. Departamento de Matemática, U.T.A.D., 5000, Vila Real, Portugal

    E. Giraldes

  3. Centro de Matemática, Universidade do Minho, 4710-057, Braga, Portugal

    P. Marques-Smith & P. Mendes Martins

Authors
  1. B. Billhardt
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  2. E. Giraldes
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  3. P. Marques-Smith
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  4. P. Mendes Martins
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Corresponding author

Correspondence to B. Billhardt.

Additional information

Communicated by László Márki.

Research supported by the Portuguese Foundation for Science and Technology (FCT) through the research program POCTI.

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Billhardt, B., Giraldes, E., Marques-Smith, P. et al. Associate inverse subsemigroups of regular semigroups. Semigroup Forum 79, 101–118 (2009). https://doi.org/10.1007/s00233-009-9150-4

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  • DOI: https://doi.org/10.1007/s00233-009-9150-4

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