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Defining relations for idempotent generators in finite partial transformation semigroups

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Abstract

We give a presentation for the semigroup of all singular partial transformations on a finite set, in terms of the generating set consisting of all idempotent partial transformations of corank 1.

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Notes

  1. The corank of a partial transformation α is n−|im(α)|, where im(α) denotes the image of α.

References

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Authors and Affiliations

  1. School of Computing, Engineering and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, NSW 2751, Australia

    James East

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  1. James East
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Correspondence to James East.

Additional information

Communicated by László Márki.

Dedicated to the memory of John M. Howie.

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East, J. Defining relations for idempotent generators in finite partial transformation semigroups. Semigroup Forum 89, 72–76 (2014). https://doi.org/10.1007/s00233-013-9512-9

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  • DOI: https://doi.org/10.1007/s00233-013-9512-9

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