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Two Examples of Diagonal Bi-Acts

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Abstract

An example of a right cancellative semigroup is constructed such that the diagonal bi-act of this semigroup is cyclic. Moreover, it is proved that every semigroup can be isomorphically embedded into a semigroup such that its diagonal bi-act of second order is cyclic, but the diagonal bi-act of third order is not finitely generated.

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References

  1. P. Gallagher, “On the finite and non-finite generation of diagonal acts,” Commun. Algebra, 34, 3123–3137 (2006).

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Authors and Affiliations

  1. National Research University of Electronic Technology, Moscow, Russia

    T. V. Apraksina, I. V. Barkov & I. B. Kozhukhov

Authors
  1. T. V. Apraksina
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  2. I. V. Barkov
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  3. I. B. Kozhukhov
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Correspondence to T. V. Apraksina.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 3–9, 2013.

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Apraksina, T.V., Barkov, I.V. & Kozhukhov, I.B. Two Examples of Diagonal Bi-Acts. J Math Sci 206, 457–461 (2015). https://doi.org/10.1007/s10958-015-2324-6

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  • DOI: https://doi.org/10.1007/s10958-015-2324-6

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