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The idempotent-separating degree of a block-group

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Abstract

In this note we characterize the least positive integer n such that there exists an idempotent-separating homomorphism from a finite block-group S into the monoid of all partial transformations of a set with n elements. In particular, as for a fundamental semigroup S this number coincides with the smallest size of a set for which S can be faithfully represented by partial transformations, we obtain a generalization of Easdown’s result established for fundamental finite inverse semigroups.

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Authors and Affiliations

  1. Departamento de Matemática, F.C.T., Universidade Nova de Lisboa, 2829-516, Monte da Caparica, Portugal

    Vítor H. Fernandes

  2. Centro de Álgebra, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    Vítor H. Fernandes

Authors
  1. Vítor H. Fernandes
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Correspondence to Vítor H. Fernandes.

Additional information

Communicated by Mikhail Volkov.

The author gratefully acknowledges support of FCT and FEDER, within the project POCTI-ISFL-1-143 of CAUL, and the fellowship SFRH/BSAB/244/2001.

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Fernandes, V.H. The idempotent-separating degree of a block-group. Semigroup Forum 76, 579–583 (2008). https://doi.org/10.1007/s00233-008-9043-y

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  • DOI: https://doi.org/10.1007/s00233-008-9043-y

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