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Two Examples of Diagonal Bi-Acts


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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  1. 1.

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

    Article  MATH  MathSciNet  Google Scholar 

  2. 2.

    P. Gallagher and N. Ruškuc, “Generation of diagonal acts of some semigroups of transformations and relations,” Bull. Aust. Math. Soc., 72, 139–146 (2005).

    Article  MATH  Google Scholar 

  3. 3.

    M. Kilp, U. Knauer, and A. V. Mikhalev, Monoids, Acts and Categories, Walter de Gruyter, Berlin (2000).

    Book  MATH  Google Scholar 

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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).

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