A cancellative amenable ascending union of nonamenable semigroups
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 687-690
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We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable.
We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable.
DOI : 10.1007/s10587-011-0039-5
Classification : 20M99, 43A07, 43A17
Keywords: amenability; semigroups; ascending union
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Donnelly, John. A cancellative amenable ascending union of nonamenable semigroups. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 687-690. doi: 10.1007/s10587-011-0039-5

[1] Banach, S.: Sur la problème de la mesure. Fundamenta math. 4 (1923), 7-33.

[2] Day, M. M.: Amenable semigroups. Ill. J. Math. 1 (1957), 509-544. | DOI | MR | Zbl

[3] Day, M. M.: Semigroups and amenability. (Semigroups, Proc. Sympos. Detroit, Michigan, 1968), pp. 5-53, Academic Press, New York (1969). | MR | Zbl

[4] Donnelly, J.: An amenable ascending union of non-amenable semigroups. Int. J. Algebra Comput. 17 (2007), 179-185. | DOI | MR | Zbl

[5] Følner, E.: On groups with full Banach mean value. Math. Scand. 3 (1955), 243-254. | DOI | MR

[6] Frey, A. H.: Studies on Amenable Semigroups. PhD thesis, University of Washington (1960). | MR

[7] Grigorchuk, R. I.: Growth and amenability of a semigroup and its group of quotients. Semigroup theory and its related fields, Proc. Int. Symp., Kyoto/Jap. (1990), 103-108. | MR | Zbl

[8] Grigorchuk, R. I.: Invariant measures on homogeneous spaces. Ukr. Math. J. 31 (1980), 388-393. | DOI | MR | Zbl

[9] Grigorchuk, R. I., Stepin, A. M.: On amenability of semigroups with cancellation. Mosc. Univ. Math. Bull. 53 (1998), 7-11. | MR | Zbl

[10] Hausdorff, F.: Grundzüge der Mengenlehre. Leipzig (1914).

[11] Hochster, M.: Subsemigroups of amenable groups. Proc. Am. Math. Soc. 21 (1969), 363-364. | DOI | MR | Zbl

[12] Klawe, M.: Semidirect product of semigroups in relation to amenability, cancellation properties, and strong Følner conditions. Pac. J. Math. 73 (1977), 91-106. | DOI | MR | Zbl

[13] Namioka, I.: Følner's conditions for amenable semi-groups. Math. Scand. 15 (1964), 18-28. | DOI | MR | Zbl

[14] Neumann, J. Von: Zur allgemeinen Theorie des Masses. Fundamenta 13 (1929), 73-116.

[15] Olśhanskii, A. Yu.: On the problem of the existence of an invariant mean on a group. Russ. Math. Surv. 35 (1980), 180-181. | DOI | MR

[16] Sorenson, J.: Existence of Measures that are Invariant Under a Semigroup of Transformations. PhD thesis, Purdue University (1966). | MR

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