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Diagonal bi-acts over semigroups with finiteness conditions

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Abstract

We present necessary conditions for the diagonal bi-act \(_S(S\times S)_S\) over an epigroup \(S\) to be finitely generated. They imply that this bi-act is not finitely generated whenever \(S\) is infinite and locally finite. This solves a problem posed by Gallagher.

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Acknowledgments

The second author was supported in part by the NSF Grant DMS 1161294.

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Authors and Affiliations

  1. National Research University “MIET”, Moscow, 124498, Russia

    I. B. Kozhukhov

  2. Department of Mathematics, Vanderbilt University, Nashville, 37240, USA

    A. Yu. Olshanskii

  3. Moscow State University, Moscow, 119991, Russia

    A. Yu. Olshanskii

Authors
  1. I. B. Kozhukhov
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  2. A. Yu. Olshanskii
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Correspondence to I. B. Kozhukhov.

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Communicated by Mikhail Volkov.

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Kozhukhov, I.B., Olshanskii, A.Y. Diagonal bi-acts over semigroups with finiteness conditions. Semigroup Forum 91, 538–542 (2015). https://doi.org/10.1007/s00233-014-9661-5

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  • DOI: https://doi.org/10.1007/s00233-014-9661-5

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