Geodesic
Bidiagonal ranks of completely (0-)simple semigroups
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 144-148.

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A bidiogonal act over a semigroup is a two-sided act, where the semigroup acts on its Cartesian power. A bidiagonal rank of a semigroup is the least power of a generating set of the bidiagonal act over this semigroup. In this paper we compute bidiagonal ranks of completely (0-)simple semigroups.
Keywords: act over a semigroup, diagonal rank, completely (0-)simple semigroup. 
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Ilia V. Barkov. Bidiagonal ranks of completely (0-)simple semigroups. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 144-148. http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a1/

[1] M. Kilp, U. Knauer, A. V. Mikhalev, Monoids, acts and categories, W. de Gruyter, Berlin–New York, 2000 | MR | Zbl

[2] V. K. Kartashov, “Independent systems of generators and the Hopf property for unary algebras”, Diskretn. Mat. i Pril., 20:4 (2009), 79–84 (in Russian) | DOI | MR

[3] E.F. Robertson, N. Ruškuc, M.R. Thomson, “On finite generation and other finiteness conditions for wreath products semigroups”, Comm. Algebra, 30:8 (2002), 3851–3873 | DOI | MR | Zbl

[4] M.R. Thomson, Finiteness Conditions of Wreath Products of Semigroups and Related Properties of Diagonal Acts, PhD thesis, University of St. Andrews, 2001

[5] P. Gallagher, “On the finite and non-finite generation of diagonal acts”, Comm. Algebra, 34:9 (2006), 3123–3137 | DOI | MR | Zbl

[6] P. Gallagher, N. Ruškuc, “Finite generation of diagonal acts of some infinite semigroups of transformations and relations”, Bull. Austral. Math. Soc., 72:1 (2005), 139–146 | DOI | MR | Zbl

[7] T. V. Apraksina, “Diagonal acta over semigroups of isotone transformations”, Chebysh. sbornik, 12:1 (2011), 10–16 (in Russian) | MR | Zbl

[8] T. V. Apraksina, I. V. Barkov, I. B. Kozhukhov, “Diagonal ranks of semigroups”, Semigroup Forum, 90:2 (2015), 386–400 | DOI | MR | Zbl

[9] I. V. Barkov, R. R. Shakirov, “Finite semigroups with minimal diagonal rank”, Mat. vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona, 16 (2014), 55–63 (in Russian)

[10] A. H. Clifford, G. B. Preston, Algebraic Theory of Semigroups, American Mathematical Soc., Providence, R.I., 1967 | MR | Zbl