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Characterization of Simplicity and Cancellativity in βS

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Abstract

We determine precisely when the Stone-Cech compactification βS of a discrete semigroup S is simple and when it is left cancellative or right cancellative. As a consequence we see that βS is cancellative only when it is trivially so. That is, βS is cancellative if and only if S is a finite group.

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Authors and Affiliations

  1. Department of Mathematics, Howard University, Washington, DC 20059, USA

    Neil Hindman

  2. Mathematics Centre, University of Hull, Hull HU6 7RX, UK

    Dona Strauss

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  1. Neil Hindman
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  2. Dona Strauss
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Correspondence to Neil Hindman or Dona Strauss.

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Hindman, N., Strauss, D. Characterization of Simplicity and Cancellativity in βS. Semigroup Forum 75, 70–76 (2007). https://doi.org/10.1007/s00233-006-0666-6

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  • DOI: https://doi.org/10.1007/s00233-006-0666-6

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